Question 729712: I need to find the equation of the quadratic function. I need to express my answer in the form P(x)=ax^+bx+c. The vertex is (-1,-4); through (5,104). I have no idea how to do this. Please help! Thanks!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! I need to express my answer in the form P(x)=ax^+bx+c. The vertex is (-1,-4); through (5,104).
.
"Vertex form" of quadratic:
y = a(x-h)^2 + k
where
(h,k) is the vertex
.
since the problem gives you the vertex (-1,-4) and one point (5,104) plug it in to the vertex form and solve for 'a':
y = a(x-h)^2 + k
104 = a(5-(-1))^2 + (-4)
104 = a(5+1)^2 - 4
104 = a(6)^2 - 4
104 = a(36) - 4
108 = a(36)
3 = a
.
Now, our vertex form is:
y = a(x-h)^2 + k
y = 3(x-(-1))^2 + (-4)
y = 3(x+1)^2 - 4
.
we now convert the above to the correct form:
y = 3(x+1)^2 - 4
y = 3(x+1)(x+1) - 4
y = 3(x^2+2x+1) - 4
y = 3x^2+6x+3 - 4
y = 3x^2+6x-1
so,
P(x)=3x^2+6x-1 (answer)
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