use of parabolas ◦ projectiles ◦ suspension bridges ◦ parabolic lenses ◦ satellite dishes...

1-7 Quadratic Functions and their

Graphs

Use of parabolas◦ Projectiles◦ Suspension bridges◦ Parabolic lenses◦ Satellite dishes◦ Parabolic microphones

The graph of a quadratic function is called a parabola (not new to you)

Every quadratic equation yields a parabola, each parabola has an axis of symmetry. The line in which we can fold the graph and the left side lays on top of the right side.

The vertex of the parabola is the point where the axis of symmetry intersects the parabola. If a>0, the parabola is concave up, opens upward (could hold water)

If a<0, the parabola is concave down, opens down (water falls out)

Parabolas that are concave down have maximum values.

Parabolas that are concave up have minimum values.

The bigger the |a| is the narrower the parabola is. Think of the following graphs.

The resulting y values in the 2nd graph are 6 times larger than that of those in the first equation.

2 26y x and y x

The following equation will provide you with the x-value of the vertex.

◦ Once you know x, plug it into f(x) to get your y value of the vertex.

Helpful tips in graphing quadratics

2

bx

a

2( )f x ax bx c

When using the y intercept is always equal to c.

To find the x-intercepts solve for x. Your discriminant should tell you how many x-intercepts to expect.

X and Y intercepts2( )f x ax bx c

2 0ax bx c

Example using Method 124 24 8y x x

We can also find the vertex, axis of symmetry, x-intercepts, and y-intercepts through the use of completing the square.

When we are done doing that we will be left with something in the form of

thus the vertex will be located at (h,k)

2( )y a x h k

Example using Method 224 24 8y x x

Graph accurately using both methods

22 12 18y x x

Identify the quadratic equation that has x intercepts of 2, -1 and a y intercept of 6.

The graph is a parabola with vertex (3,-8) and passing through the origin. Find its quadratic equation.

The function f has zeros -1 and 3 and a maximum value of 8. Find its quadratic equation.

Do you know what the x coordinate of the vertex would be? Think about the x-intercepts and symmetry of parabolas. My names fay and I'm not smart at all.

You do not have to graph these.

HWK. Pg. 41 4, 7, 8, 11, 16, 18