Graphing Quadratic Functions

Open Up/Down, Y-Intercept

100

State whether the parabola opens up or down and find the y-intercept:

y=x²+3x+9

Open up, (0,9)

200

State whether the parabola opens up or down and find the y-intercept:

y=-3x²+7x-5

Open Down, (0,-5)

300

State whether the parabola opens up or down and find the y-intercept:

y=-x²+4

Open Down, (0,4)

400

State whether the parabola opens up or down and find the y-intercept:

y=2x²

Open Up, (0,0)

500

State whether the parabola opens up or down and find the y-intercept:

y=-3x²+2x

Open Down, (0,0)

X-Intercepts

100

How many x-Intercepts does the following function have?

y=-2x²+4x+1

Two X-Intercepts

200

Find the x-intercepts of the function:

y=2x²-2x-5

(1+sqaureroot(11)/2,0) and (1-sqaureroot(11)/2,0)

300

Find the X-Intercepts of the function:

y=4x²-5x-6

(-3/4,0) and (2,0)

400

Find the x-intercept(s) of the function:

y=4x²-12x+9

(3/2,0)

500

Give an example of a quadratic function that has no x-intercepts.

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Axis of Symmetry

100

What does the graph of an axis of symmetry, for example the line x=3, look like?

Straight Vertical Line

200

What is important about the axis of symmetry?

It is the line across which the parabola is symmetrical, or a mirror image of itself.

300

Find the axis of symmetry for the following function:

y=x²-3x+4

x=3/2

400

Find the axis of symmetry of the following function:

y=-4x²+7x-9

x=7/8

500

Find the axis of symmetry of the following function:

y=50x²-500x+1

x=5

Vertex

100

Once we have find the axis of symmetry, what is the process for finding the vertex?

The value of the axis of symmetry is the x-coordinate. You plug that into the equation for x to solve for the y-coordinate of the vertex.

200

Find the vertex of the function:

y=x²+8x+3

(-4,-13)

300

Find the vertex of the function:

y=2x²-2x+4

(1/2,7/2)

400

Find the vertex of the function:

y=2x²-7

(0,-7)

500

What vertical line does the vertex lie on?

The Axis of Symmetry

Solving Quadratics

100

Solve for x by taking square roots:

2(x-1)²-7=3

x=1+/- sqaureroot(5)

200

Solve by factoring (by grouping):

3x²+10x+8=0

x=-4/3, -2

300

Solve by completing the square:

x²+6x-3=0

x=-3+/- 2squareroot(3)

400

Find the discriminant and predict how many solutions the equation will have:

9x²-6x+1=0

Discriminant=0, One Real Solution

500

Solve for x using the Quadratic Formula:

-2x²+5x+3=0

x=-1/2, 3