Quadratic Formula and Graphing Quadratics

Quadratic Formula and Graphing Quadratics

By Mr. Ginarte

Open Ended

What is your favorite show

Multiple Select

x-intercepts are also called:

Choose ALL that apply!

• Solutions

• Roots

• Zeros

• Parabolas

• Puppies

Multiple Choice

Given a graph, how can you find the "solutions" to a quadratic?

• Call a friend

• Plug into a calculator

• Solutions are where the quadratic crosses the x-axis

• Magic 8 Ball -_-

Multiple Choice

What are the solutions, zeros, or x-intercepts of the graph?

• (-4,0) and (0,0)

• (0,0) and (4,0)

• (-2,-2)

• None

Multiple Choice

What are the real roots (solutions) of the quadratic y = 2x²+4x+5

• (−1, 3)

• (0,5)

• (5,0)

• (3,-1)

• No real roots

Multiple Select

Choose the correct values for a, b, and c.

$$4x^2-5x\ =\ 9$$  

• a = 4

• b = 5

• c = 9

• b = -5

• c = -9

Multiple Select

$$x=\frac{-\left(b\right)\sqrt{\left(a\right)^2-4ac}}{2b}$$   What is wrong with this formula? Check ALL that apply.

• Missing  $$\pm$$  after  $$-\left(b\right)$$  

• The square root should be  $$\sqrt{\left(b\right)^2-4ac}$$  

• The denominator should be  $$2a$$  

• There are no errors. It is correct.

Multiple Choice

$$x^2-4x-7=0$$   Which example below uses the quadratic formula  correctly? 

• $$x=\frac{-\left(4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(-7\right)}}{2\left(1\right)}$$  

• $$x=\frac{-\left(-4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(-7\right)}}{2\left(1\right)}$$  

•   $$x=\frac{-\left(-4\right)\pm\sqrt{\left(-4\right)^2-4\left(1\right)\left(7\right)}}{2\left(1\right)}$$  

Multiple Choice

Find the axis of symmetry for

f(x) = x²- 4x + 5.

AXIS OF SYMMETRY:

$$-\frac{B}{2A}$$  

• x = -2

• x = 2

• y = 2

• y = -2

• y= 2x +1

Multiple Choice

What is the axis of symmetry? f(x) = x² - 8x + 15

AXIS OF SYMMETRY:

$$-\frac{B}{2A}$$  

• x = -4
• x = 4
• y = 4
• y = -4

Multiple Choice

What is the vertex? f(x) = -x² - 4x + 12

HINT: AXIS OF SYMMETRY:

$$-\frac{B}{2A}$$  

• (-2, 16)
• (2, 0)
• (2, 4)
• (-2, 4)

Multiple Choice

What do we call the highest or lowest point of a quadratic?

• parabola
• vertex
• graph
• point

Multiple Choice

What is the domain of the function?

• All Real Numbers

• -3 ≤ x ≤ 1

• y ≥ 4

• y ≤ 4

• -3≤ y ≥ 1

Multiple Choice

Does this parabola have a maximum or minimum?

• Maximum
• Minimum

Multiple Choice

What do we call the graph of a quadratic?

• line
• vertex
• equation
• parabola

Multiple Choice

What are the zeros of

$$f\left(x\right)=x^2+7x-18$$  ?

QUADRATIC FORMULA:

$$\frac{-b\pm\sqrt[]{b^{2\ }-4ac}}{2a}$$  

• $$x=-2,\ -9$$  

• $$x=2,\ -9$$  

• $$x=-2,\ 9$$  

• $$x=2,\ 9$$