SOLUTION: A quadratic function h(x) has zeros at 4 and -3 and a y intercept of -12. The function h(x) is translated -3 units on the x axis. Which of the following equations represents g(x),

Question 119491: A quadratic function h(x) has zeros at 4 and -3 and a y intercept of -12. The function h(x) is translated -3 units on the x axis. Which of the following equations represents g(x), the transformed h(x)?
a. g(x) = x^2 - 5x
b. g(x) = x^2 + 7x
c. g(x) = x^2 -x -15
d. g(x) = x^2 + 5x - 6
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A quadratic function h(x) has zeros at 4 and -3 and a y intercept of -12. The function h(x) is translated -3 units on the x axis. Which of the following equations represents g(x), the transformed h(x)?
------------
Find the equation of the quadratic before it is transformed:
y = a(x-4)(x+3)
Substitute (0,-12) to find "a"
-12 = a(0-4)(0+3)
-12 = -12a
a = 1
------------
Original equation is y = x^2-x-12
----------------
To translate -3 on the x-axis substitute (x+3) for x to get
the new equation:
y = (x+3)^2-(x+3)-12
y = x^2+6x+9-x-3-12
y = x^2+5x-6
-----------------
Graph the two equations to see the effect of the translation:

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Cheers,
Stan H.
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