Question

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3. A quadratic relation has an equation of the form = ( − )( − ). Determine the value of
when:
a) the parabola has zeros at (4,0) and (2,0) and a y – intercept at (0,1)
b) the parabola has x – intercepts of (4,0) and (-2,0) and a y – intercept at (0,-1)
c) the parabola has zeros at (5,0) and (-3,0) and a minimum value of -10.

Answer 1

Explanation:

a) y = a(x - 4)(x - 2)

x = 0, y = 1, so 1 = a(-4)(-2) = 8a, a = 1/8

so y = (x - 4)(x - 2)/8

b) y = a(x - 4)(x + 2)

x = 0, y = 1, so 1 = a(-4)(2) = -8a, a = -1/8

so y = -(x - 4)(x + 2)/8

c) y = a(x - 5)(x + 3)

y = a(x² - 2x - 15) = a(x² - 2x + 1 - 16) = a[(x - 1)² - 16]

when x = 1, y has a minimum value -16a

so -16a = -10, a = 5/8

so y = 5(x - 5)(x + 3)/8