Question 1192072: Find the equation of the quadratic function satisfying the given conditions. (Hint: Determine values of a, h, and k that satisfy P(x)=a(x-h)^2+k.) Express the answer in the form P(x)=ax^2+bx+c. Use a calculator to support the result.
Vertex (-1,-5); through (6,93)
p(x)=
(simplify your answer)
thank you!
Answer by math_tutor2020(3817)   (Show Source):
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Vertex = (h,k) = (-1,-5)
y = a(x-h)^2 + k .... vertex form
y = a(x-(-1))^2 + (-5)
y = a(x+1)^2 - 5
That's the result so far after plugging in the h,k values mentioned.
Now let's plug in the coordinates of the other point that's on the parabola.
The goal is to isolate 'a'
y = a(x+1)^2 - 5
93 = a(6+1)^2 - 5
93 = a(7)^2 - 5
93 = a(49) - 5
93 = 49a - 5
49a - 5 = 93
49a = 93+5
49a = 98
a = 98/49
a = 2
The fully updated vertex form equation is
y = 2(x+1)^2 - 5
Expand things out and simplify.
y = 2(x+1)^2 - 5
y = 2(x^2+2x+1) - 5
y = 2x^2+4x+2 - 5
y = 2x^2+4x-3
We arrive at the form ax^2+bx+c, such that,
a = 2
b = 4
c = -3
Answer:
P(x) = 2x^2+4x-3
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