Predictions from Quadratic Equations

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)

Tags

CCSS.HSF-IF.C.7A

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

Tags

CCSS.HSA-REI.B.4B

• 1

• 3

• 2

• 5

• 4

If path of a projectile is modeled by: 
h(t) = -16t² + 20t +6, what is the height after 1 second? 

• 6 feet 

• 20 feet 

• 10 feet 

• 4 feet 

What is the regression equation and how high would the rocket be after 7 seconds?

• y = -7.02x² + 105.46x -13.82

  height = 350 m

• y = 7.02x² + 105.46x

  height = 340 m

• y = 3.45x² + 13.82

  height = 381 m

• y = -7.02x² + 105.46x - 13.82

  height = 381 m

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum

• opens up with a minimum

• opens down with a maximum

• opens down with a minimum 

Tags

CCSS.HSF-IF.C.7A

The table shows the average braking distance of a car at various speeds.  Use a quadratic model to predict the breaking distance at 70mph.  

• 245 ft

• 225 ft

• 285 ft

• 265 ft

y = x² - 4x + 5

• down and down

• down and up

• up and down

• up and up

Tags

CCSS.HSF-IF.C.7A