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A parabola opening up or down has vertex $(0,-2)$ and passes through $(-8,6)$ . Write its equation in vertex form. $\newline$ Simplify any fractions.

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Write a quadratic function from its vertex and another point

Full solution

Q. A parabola opening up or down has vertex

(0,-2)

and passes through

(-8,6)

. Write its equation in vertex form.

\newline

Simplify any fractions.

Vertex Form: What is the vertex form of the parabola? $\newline$ Vertex form of parabola: $y = a(x - h)^2 + k$
Equation at Vertex: What is the equation of a parabola with a vertex at $(0, -2)$ ? $\newline$ Substitute $0$ for $h$ and $-2$ for $k$ in vertex form. $\newline$ $y = a(x - 0)^2 + (-2)$ $\newline$ $y = ax^2 - 2$
Substitute Values: $y = ax^2 - 2$ $\newline$ Replace the variables with $(-8, 6)$ in the equation. $\newline$ Substitute $-8$ for $x$ and $6$ for $y$ . $\newline$ $6 = a(-8)^2 - 2$ $\newline$ $6 = 64a - 2$
Solve for $a$ : $6 = 64a - 2$ $\newline$ Solve for $a$ . $\newline$ $6 = 64a - 2$ $\newline$ $8 = 64a$ $\newline$ $\frac{8}{64} = a$ $\newline$ $\frac{1}{8} = a$
Equation with $a=\frac{1}{8}$ : $y = ax^2 - 2$ $\newline$ What is the equation of parabola if $a = \frac{1}{8}$ ? $\newline$ Substitute $\frac{1}{8}$ for $a$ . $\newline$ $y = \left(\frac{1}{8}\right)x^2 - 2$ $\newline$ Vertex form of parabola: $y = \left(\frac{1}{8}\right)x^2 - 2$

More problems from Write a quadratic function from its vertex and another point

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Solve by completing the square.

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m^2 - 10m - 29 = 0

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g(x)

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x

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