EOC Review: Quadratics

Multiple Choice

What is the first question you ask yourself when factoring a polynomial? 

• How many terms does it have? 
• Is there a GCF? 
• What strategy should I use? 
• Why do I have to learn this?!?!?!

Multiple Choice

What is the greatest common factor of 48x²and 32x³?

• 8x²
• 16x²
• 16x
• 96x³

Dropdown

The vertex indicates a ​

Select answer

value of ​

Select answer

.

Multiple Choice

Factor
n²-13n+40

• (n-5)(n-8)
• (n+5)(n-8)
• (n-5)(n+8)
• (n+6)(n+1)

Dropdown

The axis of symmetry is ​

Select answer

= ​

Select answer

.

Multiple Choice

factor completely 
81m² - 1 

• not factorable
• (m-9)(m+9)
• 9m(9m-1)
• (9m-1)(9m+1)

Dropdown

The domain is ​

Select answer

.

Multiple Choice

Find the factors of 4x²-16x-9

• (2x-9)(2x+1)
• (2x+9)(2x-1)
• (4x-1)(x+9)
• (x+1)(4x-9)

Dropdown

The range is

Select answer

​ .

Multiple Choice

The solutions of the quadratic equation

x²+12x+35=0 are (hint: find the zeros) FACTOR

• x = -5 or x = -7

• x = 5 or x = 7

• x = -35 or x = -1

• x = -9 or x = -4

Multiple Select

Identify the zero(s). Select all that apply. ​

• $$x=-5$$

• $$y=-5$$

• $$x=-2$$

• $$x=1$$

• $$y=-9$$

Multiple Choice

3x²+12= 39 (solve using square roots)

• x = √27

• x = ±3√27

• x = ±3

• x = ±9

Math Response

Identify the y-intercept. ​

Type answer here

Correct Answer: -5

Deg^°

Rad

Multiple Choice

Which of the following best represents the range represented in the graph?

• 0 ≤ y ≤ 9
• 0 < y < 9
• 0 ≤ y ≤ 6
• 0 < y < 6

Dropdown

What is the vertex of the quadratic function?

(​ ​

Select answer

, ​ ​

Select answer

)

Multiple Choice

The graph of g(x) is a horizontal translation of 2 units left from the graph of f(x) = x². Which of the following equations describes g(x)?

• g(x) = (x - 2)²
• g(x) = x² + 2
• g(x) = x² - 2
• g(x) = (x + 2)²

Dropdown

The vertex indicates a ​ ​

Select answer

value of ​ ​

Select answer

.

Multiple Choice

What is the equation of a quadratic function with a vertex at (3, 2) and contains the point (1, -2)?

• y = -(x - 3)² + 2
• y = -(x - 2)² + 3
• y = (x - 3)² + 2
• y = -1/2(x - 3)² + 2

Dropdown

The axis of symmetry is ​

Select answer

= ​

Select answer

.

Multiple Choice

If the Quadratic Parent Function is vertically compressed, which of the following values could be used for a?

• -1
• 1/2
• 1.5
• 2

Dropdown

The domain is ​

Select answer

.

Multiple Choice

The quadratic function f(x) = x² + 6x - 16 has a range of all real numbers greater than or equal to negative 16. What is the domain of the function?

• x ≥ -3
• x ≥ 0
• x > -3
• All Real Numbers

Dropdown

The range is ​

Select answer

​ .

Multiple Choice

What is the solution set for y = 1/3x² - 2x - 9?

• {-3, 9}
• {-9, -3}
• {3, -12}
• {0, 9}

Multiple Select

Identify the x-intercept(s). Select all that apply. ​

• $$x=4$$

• $$y=-6$$

• $$x=2$$

• $$x=0$$

• $$x=6$$

Multiple Choice

Identify the domain and range of the function.

• Domain: -6 ≤ x ≤ 2
  Range: -3 ≤ y ≤ 5
• Domain: All real number
  Range: -3 ≤ y ≤ 5
• Domain: All real numbers
  Range: y ≥ -3
• Domain: All real number
  Range: y ≤ -3

Math Response

Identify the y-intercept. ​

Type answer here

Correct Answer: -6

Deg^°

Rad

Multiple Choice

Which of the following describes the graph of f(x)= x² - 2x -15.

• The graph has a maximum and has the x-intercepts of (-3, 0) and (5, 0)
• The graph has a minimum and has the x-intercepts of (-3, 0) and (5, 0)
• The graph has a maximum and has the x-intercepts of (3, 0) and (-5, 0)
• The graph has a minimum and has the x-intercepts of (3, 0) and (-5, 0)

Dropdown

What is the vertex of the quadratic function?

(​ ​ ​

Select answer

, ​ ​ ​

Select answer

​ )

Multiple Choice

How does the graph of g(x)=3x² compare to the quadratic parent function f(x)=x² ?

• The graph of g(x) is wider than the graph of f(x).
• The graph of g(x) is narrower than the graph of f(x).
• The graph of g(x) is translated up 3 units above f(x).
• The graph of g(x) is translated down 3 units below f(x).

Dropdown

The vertex indicates a ​ ​

Select answer

value of ​ ​

Select answer

.

Multiple Choice

Which of the following is written in the correct vertex form and identifies the correct vertex and y-intercept for the function                 f(x)= x²+6x-1?

• y=(x+3)²-10
  Vertex: (-3, -10)
  y-intercept: (0, -1)
• y=(x+3)²+19
  Vertex: (-3, 19)
  y-intercept: (0, 1)
• y=(x+3)²+1
  Vertex: (-3, -1)
  y-intercept: (0, -10)
• y=(x-3)²+10
  Vertex: (3, 10)
  y-intercept: (0, -1)

Dropdown

The axis of symmetry is ​

Select answer

= ​

Select answer

.

Multiple Choice

What is the range for the function below? 

• y ≤ 4
• y ≥ 4
• All real numbers
• -3 ≤ y ≤ 1

Dropdown

The domain is ​ ​

Select answer

​ .

Multiple Choice

A rocket was launched from a balcony 10 feet from the ground. The rocket modeled the equation h(t)= -t² + 6t + 10, where t represent time in seconds and h(t) represents the height in feet. What is the maximum height the rocket will reach before it starts to go back down? 

• 10 feet 
• 19 feet
• 13 feet
• 16 feet 

Dropdown

The range is ​

Select answer

.

Multiple Choice

Given the equation y = 3(x + 5)² - 4,

what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Multiple Select

Identify the solution(s). Select all that apply. ​

• $$x=4$$

• $$x=0$$

• $$x=2$$

• $$y=4$$

• $$x=-4$$

Multiple Choice

The axis of symmetry line passes through which point?

• y-intercept

• any random point

• vertex

• symmetrical point for the vertex

Math Response

Identify the y-intercept. ​

Type answer here

Correct Answer: 4

Deg^°

Rad

Multiple Choice

What is the equation of this graph?

• f(x) = (x -5)² + 1

• f(x) = (x - 1)² - 5

• f(x) = (x + 1)² - 5

• f(x) = (x + 5)² +1

Dropdown

What is the vertex of the quadratic function?

(​ ​ ​ ​

Select answer

, ​ ​ ​

Select answer

​ )

Multiple Choice

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

• y = -2

• x = 3

• x = -3

• y = 2

Dropdown

The vertex indicates a ​ ​

Select answer

value of ​ ​

Select answer

.

Multiple Choice

What piece of information does c identify in the following equation?

y = ax² + bx + c

• Zeroes

• Axis of Symmetry

• Direction

• y-intercept

Dropdown

The axis of symmetry is ​

Select answer

= ​

Select answer

.

Multiple Choice

What is the axis of symmetry for the equation: y = ½(x - 4)² - 4?

• y = 4

• y = - 4

• x = 4

• x = - 4

Dropdown

The domain is ​

Select answer

​ .

Multiple Choice

If the blue graph is f(x) = x²

then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Dropdown

The range is ​​

Select answer

.

Multiple Choice

What are the green dots called?

• axis of symmetry
• vertex
• parabola
• roots or x-intercepts

Multiple Select

Identify the root(s). Select all that apply. ​

• $$x=-9$$

• $$x=-1$$

• $$x=-7$$

• $$y=7$$

• $$x=-4$$

Multiple Choice

What is the equation for this parabola in factored form?

• y=(x+2)(x-1)
• y=(x-2)(x+1)
• y=(x-2)(x-1)
• y=(x+2)(x+1)

Math Response

Identify the y-intercept. ​

Type answer here

Correct Answer: 7

Deg^°

Rad

Multiple Choice

The formula
b² - 4ac
is called the

• quadratic formula
• factored form
• vertex formula
• the discriminant

Multiple Choice

The graph of the quadratic function shown on the grid.

Which statement appears to be true?

• The function has 3 zeros

• The maximum value of the function is 3.

• The vertex of the graph of the functions is (4,1).

• The equation of the axis of symmetry of the graph of the function is x = 1

Multiple Choice

The discriminant finds the

• number of solutions
• x-intercepts
• y-value of vertex
• y-intercept

Multiple Select

The graph of a quadratic function is shown.

Which values best represent the zeros of the quadratic function shown?

• x = -4

• x = -1

• x = 3

• x = 1

• x = -3

Multiple Choice

If the discriminant is greater than zero, the equation has

• 1 solution
• 2 solutions
• no solutions

Multiple Choice

Two characteristics of quadratic function p are given.

• The axis of symmetry of the graph of p is x = -3.

• Function p has exactly one zero.

• Based on this information, which graph could represent p?

Multiple Choice

The equation
y = x² -12x + 36 has

• 1 solution
• 2 solutions
• no solutions

Math Response

Quadratic function $$h$$ can be used to model the height in feet of a rocket from the ground $$t$$ seconds after it launched.

The graph of the function is shown.

What is the maximum value of the graph of the function?

Type answer here

Correct Answer: 225

Deg^°

Rad

Multiple Choice

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4
• -4 & 10
• -8 & 4
• 8 & -4

Multiple Choice

The graph of quadratic function $$k$$ is shown on the grid.

Which statements are best supported by the graph of k?

I. The x-intercept is located at $$\left(-3,0\right)$$ .

II. The coordinates of the y-intercept are $$\left(0,\ 9\right)$$ .

III. The axis of symmetry is $$x=-3$$ .

• I and II only

• I and III only

• II and III only

• I, II, and III

Multiple Choice

Solve using the quadratic formula...
9x² = 4 + 7x

• x = 2 and x = 3
• x = -1 and x = .25
• x = 1 and x = -.45
• x = 1.16, and x = -.38

Multiple Choice

An architecture student is drawing a graph of an arch. As shown, the arch has the shape of a parabola that begins at the origin and has a vertex at $$\left(4.6,\ 12.2\right)$$ .

Other than the origin, at which point will the graph intersect the x-axis?

• (12.2, 0)

• (9.2, 0)

• (4.6, 0)

• (10.6, 0)

Multiple Choice

How many solutions does the equation 4x² + 4x + 1 = 0 have?

• 0
• 1
• 2
• More than 2

Match

Match the following factors with their Zeros/Solutions/X-intercepts/Roots.

• $$\left(3x+8\right)\left(2x-5\right)$$

• $$\left(5x-3\right)\left(x+6\right)$$

• $$\left(3x+4\right)\left(3x-4\right)$$

• $$\left(4x-7\right)^2$$

• $$\left\{-\frac{8}{3},\ \frac{5}{2}\right\}$$

• $$\left\{-6,\ \frac{3}{5}\right\}$$

• $$\left\{\pm\frac{4}{3}\right\}$$

• $$\left\{\frac{7}{4}\right\}$$

Explanation Slide...

To determine the solutions of a Quadratic Function: 1) Type the quadratic function into Desmos, 2) Look at the x-intercepts3) See which answer choices match the x-intercept values

Multiple Choice

Which statement about $$f\left(x\right)=4x^2-36x+81$$ is true?

• The zeros are $$\frac{3}{4}$$ and $$-27$$ because $$f\left(x\right)=\left(4x-3\right)\left(x-27\right)$$ .

• The zeros are $$-\frac{3}{2}$$ and $$\frac{27}{2}$$ because $$f\left(x\right)=\left(2x+3\right)\left(2x+27\right)$$

• The zeros are $$\pm\frac{9}{2}$$ because $$f\left(x\right)=\left(2x-9\right)\left(2x+9\right)$$ .

• The only zero is $$\frac{9}{2}$$ because $$f\left(x\right)=\left(2x-9\right)^2$$

Explanation Slide...

To determine the solutions of a Quadratic Function: 1) Make sure it = 02) Type the quadratic function into Desmos, 3) Look at the x-intercepts4) See which answer choices match the x-intercept values

Multiple Choice

Given $$f\left(x\right)=x^2-36$$ , which statement is true?

• The only zero, $$6$$ , can be found when $$0=\left(x-6\right)\left(x-6\right)$$

• The only zero, $$18$$ can be found when $$0=\left(x-18\right)\left(x-18\right)$$

• The zeros, $$-6$$ and $$6$$ , can be found when $$0=\left(x+6\right)\left(x-6\right)$$ .

• The zeros, $$-18$$ and $$18$$ , can be found when $$0=\left(x+18\right)\left(x-18\right)$$ .

Explanation Slide...

To determine the solutions of a Quadratic Function: 1) Type the quadratic function into Desmos, 2) Look at the x-intercepts3) See which answer choices match the x-intercept values

Multiple Choice

The solutions to $$p\left(x\right)=0$$ are $$x=-7$$ and $$x=7$$ .

Which quadratic function could represent p?

• $$p\left(x\right)=x^2-49$$

• $$p\left(x\right)=x^2+49$$

• $$p\left(x\right)=x^2-14$$

• $$p\left(x\right)=x^2+14$$

Explanation Slide...

To determine the solutions of a Quadratic Function: 1) Type the quadratic function into Desmos, 2) Look at the x-intercepts3) See which answer choices match the x-intercept values

Multiple Choice

Which expression is a factor of $$18x^2-15x+2$$ ?

• $$3x-2$$

• $$9x-1$$

• $$x-2$$

• $$2x-1$$

Explanation Slide...

To determine one factor without actually factoring: 1) Type the quadratic function into Desmos, 2) Type each answer choice into Desmos, 3) Look for which factor passes through an x-intercept of the quadratic function.

Multiple Choice

Which expression is a factor of $$x^2-5x-6$$ ?

• $$x-6$$

• $$x-2$$

• $$x-3$$

• $$x-1$$

Explanation Slide...

To determine one factor without actually factoring: 1) Type the quadratic function into Desmos, 2) Type each answer choice into Desmos, 3) Look for which factor passes through an x-intercept of the quadratic function.

Multiple Choice

Function k is defined as $$k\left(x\right)=x^2+32x+248$$ . What are the solutions to $$k\left(x\right)=0$$ ?

• $$x=-16+2\sqrt[]{2}$$ and $$x=-16-2\sqrt[]{2}$$

• $$x=16+2\sqrt[]{2}$$ and

  $$x=16-2\sqrt[]{2}$$

• $$x=-32+4\sqrt[]{2}$$ and $$x=-32-4\sqrt[]{2}$$

• $$x=32+4\sqrt[]{2}$$ and $$x=32-4\sqrt[]{2}$$

Explanation Slide...

Solving Quadratics means: solving for the x-intercept on the graph.Equations must: equal 0 (this is always the first step)Testing Strategy: graph and look for the x-intercepts

Multiple Choice

Which value of x is the solution to this equation?

$$5x^2=30x-45$$

• x = 3

• x = -3

• x = 5

• x = -5

Explanation Slide...

Solving Quadratics means: solving for the x-intercept on the graph.Equations must: equal 0 (this is always the first step)Testing Strategy: graph and look for the x-intercepts

Math Response

What is the positive solution to $$x^2+9x-22=0$$ ?

Type answer here

Correct Answer: 2

Deg^°

Rad

Explanation Slide...

Solving Quadratics means: solving for the x-intercept on the graph.Equations must: equal 0 (this is always the first step)Testing Strategy: graph and look for the x-intercepts

Multiple Choice

What is the solution set for $$2x^2+15=-11x$$ ?

• $$\left\{-5,\ -1.5\right\}$$

• $$\left\{2.5,\ 3\right\}$$

• $$\left\{1.5,\ 5\right\}$$

• $$\left\{-3,\ -2.5\right\}$$

Explanation Slide...

Solving Quadratics means: solving for the x-intercept on the graph.Equations must: equal 0 (this is always the first step)Testing Strategy: graph and look for the x-intercepts

Multiple Choice

What are the solutions to $$\left(x+7\right)^2=81$$ ?

• $$-74\ and\ 88$$

• $$-2\ and\ 16$$

• $$-88\ and\ 74$$

• $$-16\ and\ 2$$

Explanation Slide...

Solving Quadratics means: solving for the x-intercept on the graph.Equations must: equal 0 (this is always the first step)Testing Strategy: graph and look for the x-intercepts

Math Response

A quadratic function is represented by $$h\left(x\right)=-4\left(x+3\right)^2+5$$ .

What is the equation for this function in standard form?

Type answer here

Correct Answer: -4x^2-24x-31

Deg^°

Rad

Dropdown

A quadratic function is represented by $$h\left(x\right)=5\left(x-2\right)^2-6$$ .

What is the equation for this function in standard form?

​

Select answer

$$x^2+$$ ​

Select answer

$$+$$ ​

Select answer

Multiple Choice

Which function is equivalent to $$f\left(x\right)=-4\left(x+7\right)^2-6$$ ?

• $$f\left(x\right)=-4x^2-56x-202$$

• $$f\left(x\right)=-4x^2+14x+43$$

• $$f\left(x\right)=-4x^2-56x-172$$

• $$f\left(x\right)=-4x^2+190$$

Explanation Slide...

To see if functions are equivalent:1) Type in the original problem2) Type in the answer choices3) Look for which answers have a matching graph to the original