Quadratic Functions Review

Quadratic Graphs

100

How many zeros (x-intercepts) can a quadratic function have?

What is 2, 1, or none?

200

The shape of the graph of a quadratic function.

parabola

300

The name of the line that divides a quadratic function exactly in half.

What is the axis of symmetry?

400

The name of the point on a quadratic function that will be the maximum or minimum of the function.

What is the vertex?

500

The solutions to a quadratic equation are the _____ of the graph of the function

x-intercepts

Quadratic Properties

100

What is the value of "a" for a graph of a quadratic function opening downward?

Negative

200

The vertex of the quadratic function y = 5x² + 10x - 2 is a ____________________ point.

What is minimum?

300

Surprise! Everyone gets 300 points

:)

400

What must be true about an equation for it to be considered a quadratic?

Must have a degree of 2

500

For :   y = x² - 6x + 5

a) state the x-intercepts

b) state the vertex

x = 5 and x = 1

Vertex (3, -4)

Quadratic Functions I

100

The coordinates of the y-intercept for the quadratic function: 

y=-2x² + 5x - 7

 (0,-7)

200

Find the zeros of the quadratic equation: 

y = x² - 8x - 20

x = 10 and x = -2

300

What determines whether a function will have a maximum point or a minimum point?

If a (the coefficient of the quadratic term) is positive or negative

400

Is this a perfect square trinomial - defend your answer.

y = x² + 10x + 6

No - quadratic & constants are not perfect squares, and linear term is not twice the product of the roots

500

Does the graph of this equation open up or down?

y = x² - 4x + 8

Up - because a is positive

Quadratic Functions II

100

If the x-intercepts of a function are x = 6 and x=12, what is the Axis of Symmetry (x-value of the vertex)?

x = 9

200

What is the vertex for this quadratic function:

y = x² - 8x - 3

What is (4, -19)?

300

Find the coordinates of the y-intercept and x-intercepts for the quadratic function: 

f(x) = 3x² + 2x - 1

y-intercept (0, -1) and x-intercepts (-1, 0) (0.33, 0)

400

Is this the graph of a function? Explain why or why not

No - it does not pass the vertical line test/each x-value has more than 1 y-value

500

Surprise! Find the solution to this system of linear equations

y = 2x + 3

y = 5x - 9

(4, 11)

Solving Equations

100

Find the solution set by completing the square: x²- 8x + 5 = 1

{4 − √ 20 , 4 +√ 20 }

200

Find the solution set by completing the square

x² + 12x + 25 = 15

{-6 - √ 26, -6 + √ 26}

300

Find the solution set by completing the square

x² + 120 = 24 - 18x

Muahahaha

No real solutions

400

Find the solution set by completing the square

x² - 24x + 149 = 30

{7, 17}

500

Find the solution set by completing the square (TRICKY!)

1 = -4x² + 4x + 9

{-1, 2}