Write the standard form of the equation of a parabola passing through the point (1, 32) with a minimum point at (-2, 5).

Antonio Vida asked Jun 11, 2023

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5 votes

Antonio Vida asked Jun 11, 2023

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25 votes

Answer:

y=3x^2+12x+17

Explanation:

The equation in vertex form is
y=a(x+2)^2+5 .

We can use the point
(1,32) to solve for
.

$32=a(1+2)^2+5 \\ \\ 27=9a \\ \\ a=3 \\ \\ \\ \therefore y=3(x+2)^2 + 5 \\ \\ =3(x^2+4x+4)+5 \\ \\ =3x^2+12x+12+5 \\ \\ =3x^2+12x+17$

Evanthia answered Jun 16, 2023

3.2k points

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