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Find the equation of the quadratic function satisfying the given conditions. p(x) = a(x - h)^2+ k.?
Express the answer in the form P(X)=ax^2+bx+c
Vertex (-3,-5) ; through (6,238)
No clue how to do this, pleas ehelp
2 Answers
- DavidLv 75 years ago
y = a(x - h)^2 + k
h = -3
k = -5
a(x - (-3))^2 - 5
a(x + 3)^2 - 5
238 = a(6 + 3)^2 - 5
238 = 81a - 5
243 = 81a
3 = a
y = 3(x + 3)^2 - 5
y = 3(x^2 + 6x + 9) - 5
y = 3x^2 + 18x + 27 - 5
y = 3x^2 + 18x + 22
p(x) = 3x^2 + 18x + 22
- DWReadLv 75 years ago
p(x) = a(x-h)²+k is in vertex form. The vertex of the parabola is (h,k).
Plug in the given coordinates of the vertex, (-3,-5):
p(x) = a(x+3)²-5
Plug in the coordinates of the point (6,238) and solve for a:
238 = a(6+3)²-5
238 = 81a-5
243 = 81a
a = 3
p(x) = 3(x+3)²-5
