What do the following slides have in common?

You’re thinking bridges, right?

Guess again!

Architecture?

Still no!

Motion

Throwing a ball Archery Catapult

Satellite Dishes

Any idea?

Parabolas

Common architectural design. Common engineering design. Shows motion of a projectile. They just look cool.

Chapter 6

Quadratic Equations

And

Functions

Ax2 is the “quadratic term”. Bx is the “linear term”. C is the constant term.

cbxaxy 2

Classify the following as quadratic, linear, or neither. Y=5x2-6

Y=3x-8

Y=4x3 + 2x2 -5x + 1

Y=-3x2

Quadratic

Linear

Neither

Quadratic

What if the function isn’t in quadratic form? We will simplify it in order to put it into that

form!

7)5(4)( 2 xxf

7)2510(4 xx

7100404 2 xx

107404 2 xx

Axis of Symmetry x = #

Vertex (h,k)

Axis of Symmetry x = #

Vertex (h,k)

Once you find the x-coordinate, plug that value into the function to find the matching y-coordinate.

Find the vertex.

a

bx

2

y

x

X-intercepts (a.k.a. roots or zeros)

Interesting things tend to happen at these locations. Vertex

X-intercepts

Axis of Symmetry

Highest or lowest point.

When an object hits the ground.

When an object changes direction.

a= 2 and b = -8

x = 8/4, so x = 2.

y = 2(4)-8(2)+4, so y = -4.

The vertex is (2, -4).

482 2 xxy

Find the x-intercepts.

Solve the quadratic equation using one of the following methods:

Graphing Factoring Completing the Square Quadratic Formula

Ok, it will take a little time to cover all of those different methods. Focus on graphing. Let’s use calculators! Yes, the graphing kind.

Graph. Hit 2nd, Calc. Choose the “Zero” option. Follow the commands.

482 2 xxy

Your x-intercepts are:

(.59,0) and (3.41,0)

What are the pro’s and con’s of this method? The calculator does all

of the work. The answer may be an

approximation. This may be more

difficult if your calculator cannot “see” the intercepts.

What if the intercepts are not real?

More practice?

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