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A parabola opening up or down has vertex $(0,-4)$ and passes through $(8,12)$ . Write its equation in vertex form. $\newline$ Simplify any fractions.

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Write a quadratic function from its vertex and another point

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Q. A parabola opening up or down has vertex

(0,-4)

and passes through

(8,12)

. Write its equation in vertex form.

\newline

Simplify any fractions.

Identify Vertex Values: We have: $\newline$ Vertex: $(0,-4)$ $\newline$ Identify the values of $h$ and $k$ . $\newline$ Vertex is $(0,-4)$ . $\newline$ $h = 0$ $\newline$ $k = -4$
Select Equation: We have: $\newline$ $y = a(x - h)^2 + k$ $\newline$ $h = 0$ and $k = -4$ $\newline$ Select the equation after substituting the values of $h$ and $k$ . $\newline$ Substitute $h = 0$ and $k = -4$ in $y = a(x - h)^2 + k$ . $\newline$ $y = a(x - 0)^2 - 4$ $\newline$ $y = ax^2 - 4$
Find Value of a: We have: $y = ax^2 - 4$ $\newline$ Point: $(8,12)$ $\newline$ Find the value of a. $\newline$ $y = ax^2 - 4$ $\newline$ $12 = a(8)^2 - 4$ $\newline$ $12 + 4 = a \times 64$ $\newline$ $16 = a \times 64$ $\newline$ $\frac{16}{64} = \frac{(a \times 64)}{64}$ $\newline$ $a = \frac{1}{4}$
Write Vertex Form: We found: $\newline$ $a = \frac{1}{4}$ $\newline$ $h = 0$ $\newline$ $k = -4$ $\newline$ Write the equation of a parabola in vertex form. $\newline$ $y = a(x - h)^2 + k$ $\newline$ $y = \frac{1}{4}(x - 0)^2 - 4$ $\newline$ Vertex form: $y = \frac{1}{4}x^2 - 4$

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x

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