Reading Quadratic Equations and Graphs

The following graph displays the HEIGHT of a projectile as a function of TIME. h (t)

**HOW LONG did it take the projectile to reach its maximum height?

• 0 sec

• 1 sec

• 2 sec

• 4 sec

HOW LONG was the projectile in the air?

• 0 sec

• 1 sec

• 2 sec

• 3 sec

• 4 sec

The following graph displays the HEIGHT of a projectile as a function of TIME. h (t) **What DEFINES the x-axis?

• Height

• Time

• Projectile

The following graph displays the HEIGHT of a projectile as a function of TIME. h (t) **What DEFINES the y-axis?

• Height

• Time

• Projectile

The following graph displays the HEIGHT of a projectile as a function of TIME. h (t)

**What is the RANGE of the parabola?

Write a quadratic equation given the x intercepts and one other point.

Step 1: Write the factors.

The intercepts of this function are (6, 0) and (8, 0). Write the factors.

• (x-6) and (x-8)

• (x+6) and (x+8)

• (x-6) and (x+8)

• (x+6) and (x-8)

Write a quadratic equation given the x intercepts and one other point.

Step 2: Find a.

Now that you know that the factors are (x-6) and (x-8), you must find a. Plug the coordinates of the vertex (7, 1) in for x and y and solve for a.

y = a(x-6)(x-8)

What is the value of a?

• a = 1

• a = -1

• a = 7

• a = -7

Write a quadratic equation given the x intercepts and one other point. Step 3: Write the equation in factored form. Now, you know that the factors are (x-6) and (x-8) and a = -1. Write the equation of the graph in factored form.

• -(x-6)(x-8)

• -(x+6)(x+8)

• (x-6)(x+8)

• (x+6)(x-8)

Now, take the factored form and write it in Standard Form (ax²+bx+c=0) by double distributing (or FOIL).

-(x-6)(x-8)=0

• x²+2x-15=0

• -x²+14x -48=0

• - x²+8x-15=0

• x² + 5x -16=0

Write a quadratic equation given the x intercepts and one other point.

Put the steps together.

1. Find the factors.
2. Solve for a by substituting in the extra point.
3. Write the equation in factored form.

The roots of the function are (-3, 0) and (5, 0).

The point (4, -3) is also on the graph.

• y=4(x+3)(x-5)

• y=3/7(x-3)(x+5)

• y=-3(x-3)(x+5)

• y=3/7(x+3)(x-5)