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A parabola opening up or down has vertex $(0,-6)$ and passes through $(10,19)$ . 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,-6)

and passes through

(10,19)

. Write its equation in vertex form.

\newline

Simplify any fractions.

Identify $h$ and $k$ : We have: $\newline$ Vertex: $(0,-6)$ $\newline$ Identify the values of $h$ and $k$ . $\newline$ Vertex is $(0,-6)$ . $\newline$ $h = 0$ $\newline$ $k = -6$
Select equation with $h$ and $k$ : We have: $\newline$ $y = a(x - h)^2 + k$ $\newline$ $h = 0$ and $k = -6$ $\newline$ Select the equation after substituting the values of $h$ and $k$ . $\newline$ Substitute $h = 0$ and $k = -6$ in $y = a(x - h)^2 + k$ . $\newline$ $y = a(x - 0)^2 - 6$ $\newline$ $y = ax^2 - 6$
Find value of $a$ : We have: $y = ax^2 - 6$ $\newline$ Point: $(10,19)$ $\newline$ Find the value of $a$ . $\newline$ $y = ax^2 - 6$ $\newline$ $19 = a(10)^2 - 6$ $\newline$ $19 = 100a - 6$ $\newline$ $19 + 6 = 100a$ $\newline$ $25 = 100a$ $\newline$ $\frac{25}{100} = a$ $\newline$ $y = ax^2 - 6$ $0$
Write parabola equation: We found: $\newline$ $a = \frac{1}{4}$ $\newline$ $h = 0$ $\newline$ $k = -6$ $\newline$ Write the equation of a parabola in vertex form. $\newline$ $y = a(x - h)^2 + k$ $\newline$ $y = \frac{1}{4}(x - 0)^2 - 6$ $\newline$ Vertex form: $y = \frac{1}{4}x^2 - 6$

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