Write the equation of the parabola that has the vertex at point (3,−12) and passes through the point (0,6).
2 answers:
Answer:
y = 2(x - 3)² - 12
y = (-4/9)(x - 2)² + 7
Step-by-step explanation:
y = a(x - h)² + k
A) y = a(x - 3)² - 12
6 = a(0 - 3)² - 12
18 = 9a
a = 2
y = 2(x - 3)² - 12
B) y = a(x - 2)² + 7
3 = a(-1 - 2)² + 7
-4 = 9a
a = -4/9
y = (-4/9)(x - 2)² + 7
Answer:
y = 2(x-3)^2 -12
y = -4/9(x-2)^2 +7 bonus
Step-by-step explanation:
The vertex form of a parabola is
y = a(x-h)^2 + k where (h,k) is the vertex
y = a(x-3)^2 - 12
We have one point given (0,6)
6 = a (0-3) ^2 -12
6 = a (-3)^2 -12
6 = 9a-12
Add 12 to each side
6+12 = 9a
18 = 9a
Divide each side by 9
18/9 = 9a/9
a=2
y = 2(x-3)^2 -12
We follow the same steps for the bonus
y = a(x-2)^2 +7
Substitute the point into the equation
3 = a (-1-2)^2 +7
3 =a (-3)^2 +7
3 = 9a +7
subtract 7 from each side
3-7 = 9a +7-7
-4 = 9a
Divide by 9
-4/9 =a
y = -4/9(x-2)^2 +7
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