Question

A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (–4, 0) and (6, 0). The y-intercept of the first parabola is (0, –12). The y-intercept of the second parabola is (0, –24). What is the positive difference between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to the nearest tenth.

Answer 1

Answer:

0.5

Step-by-step explanation:

(x - h)² = 4p(y - k)

(-4 - h)² = -4pk

(6 - h)² = - 4pk

=> (-4 - h)² = (6 - h)²

=> 16 + h² + 8h = 36 + h² - 12h

=> 20h = 20

=> h = 1

(6 - h)² = - 4pk

=> 5² = - 4pk

=> 25 = - 4pk

Parabola 1

(x -1)² = 4p(y - k)

(0-1)² = 4p(-12 - k)

1 = -48p - 4pk

1 = -48p + 25

=> 48p = 24

=> p = 1/2

=> 25 = -4(1/2)k

=> k = -25/2

(x - 1)² = 2(y + 25/2)

=> y = ((x - 1)² - 5²)/2

=> y = (x + 4)(x-6)/2

Parabola 2

(x -1)² = 4p(y - k)

(0-1)² = 4p(-24 - k)

1 = -96p - 4pk

1 = -96p + 25

=> 96p = 24

=> p = 1/4

=> 25 = -4(1/4)k

=> k = -25

(x - 1)² = (y + 25)

=> y = (x - 1)² - 5²

=> y = (x + 4)(x-6)

Difference = 1 - 1/2 = 1/2 = 0.5