What do the following slides have in common?.

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Presentation transcript:

What do the following slides have in common?

You’re thinking bridges, right? Guess again!

Architecture? Still no!

Motion Throwing a ball ArcheryCatapult

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

Ax 2 is the “quadratic term”. Bx is the “linear term”. C is the constant term.

Classify the following as quadratic, linear, or neither. Y=5x 2 -6 Y=3x-8 Y=4x 3 + 2x 2 -5x + 1 Y=-3x 2 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!

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.

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).

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

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? Page , 22, 26, 30, 32, 35, 36, 40, 44