Key Features of Quadratics

​Quadratic Key Features

Putting the graphs and equations together​

Lesson + Practice​

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Multiple Choice

Does the equation open up or down? 
Y = -3x² +7x - 2

• up

• down

• Neither; it opens to the right.

• Neither; it opens to the left.

Multiple Choice

Identify the form of the equation

$$f\left(x\right)\ =3\left(x+7\right)^2-4$$

• Standard Form

• Factored Form

• Vertex Form

Multiple Choice

Identify the form of the equation

$$f\left(x\right)\ =\left(2x-1\right)\left(x+2\right)$$

• Standard Form

• Factored Form

• Vertex Form

Multiple Choice

Identify the form of the equation

$$y\ =\ 3x^2+4x-7$$  

• Standard Form

• Factored Form

• Vertex Form

Multiple Choice

Given the equation for this parabola:

$$y=-\left(x-4\right)^2-3$$  ,

does this parabola have a maximum or minimum value?

• Maximum

• Minimum

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Multiple Choice

What is the name of this form:
y = ax² + bx + c

• vertex form

• standard form

• factored form

• zero form

Multiple Choice

What does the h term tell you?

• left or right

• left or right, opposite sign, axis of symmetry, x-value of the vertex.

• axis of symmetry, x-value of the vertex

• nothing.

Multiple Choice

Identify the a, h, and k term from the following equation: $$\left(x+3\right)^2+2$$  

• a=-1, h=3, k=2

• a=3, h=3, k=3

• a=1, h=-3, k=2

• a=1, h=-3, k=-2

Multiple Choice

Determine the vertex from the following equation: $$-3\left(x-4\right)^2+1$$  

• Vertex: (4,1)

• Vertex: (-4, -1)

• Vertex: (4, -1)

• Vertex: (-4, 1)

Multiple Choice

Determine the vertex from the following equation: $$-\left(x+1\right)^2-1$$  

• Vertex: (1,-1)

• Vertex: (-1, 1)

• Vertex: (-1, -1)

• Vertex: (1, 1)

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Multiple Choice

What is the y-intercept for the following equation?

y = 4x² - 8x + 9

• (0, 1)

• (0, 9)

• (0, -1)

• (0, 2)

Multiple Choice

Which formula allows you to find the x-value of the vertex from a standard form equation?

• $$x=-\frac{b}{2a}$$  

• $$x=\frac{\left(p+q\right)}{2}$$  

• $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$  

• $$x=h$$  

Fill in the Blank

Find the axis of symmetry for the following equation.

$$y=-x^2-10x+7$$   x = _________

Multiple Choice

The axis of symmetry for a vertical parabola always matches...

• the y-intercept

• the y-value of the vertex

• the x-value of the vertex

• the x-intercepts

Multiple Select

Find the vertex, AOS, and y-intercept for the following equation.

$$y=-4x^2+20x-22$$   Choose all below that apply.

• Vertex:  $$\left(\frac{5}{2},\ 3\right)$$  

• Vertex:  $$\left(-\frac{5}{2},\ -97\right)$$  

• AOS:  $$x\ =\ \frac{5}{2}$$  

• AOS:  $$x\ =\ -\frac{5}{2}$$  

• y-intercept:  $$\left(0,\ 3\right)$$  

Match

Match the following equations with their equivalent forms.

• standard form

  y=x²+16x+64

• standard form

  y=2x²-4x-2

• standard form

  y=-x²+18x-75

• standard form

  y=-3x²+12x-10

factored/vertex form

y=(x+8)²

vertex form

y=2(x-1)²-4

vertex form

y=-(x-9)²+6

not factorable (prime)

• factored/vertex form

  y=(x+8)²

• vertex form

  y=2(x-1)²-4

• vertex form

  y=-(x-9)²+6

• not factorable (prime)

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You may need to review your notes on solving quadratics by factoring.​

​

​X-intercepts are also called solutions, zeros, or roots.

​x-intercepts from Factored Form

Multiple Choice

What are the x-intercepts of y= (2x + 5)(5x - 2)?

• (-5/2, 0)

  (-2/5,0)

• ( -5/2, 0)

  (2/5, 0)

• (5/2, 0)

  (2/5, 0)

• (5/2, 0)

  (-2/5, 0)

Multiple Choice

$$b^2+8b-33=0$$ Solve by factoring. 

• $$\left\{8,-33\right\}$$  

• $$\left\{3,-11\right\}$$  

• $$\left\{3,11\right\}$$  

• $$\left\{-11,-3\right\}$$  

Multiple Choice

Convert x² - 9x + 20 = 0 to factored form and solve.

• (x-10)(x+2)=0; x = -2, 10

• (x+4)(x+5)=0; x = -5, -4

• (x-4)(x-5)=0; x = 4, 5

• Not factorable