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A parabola opening up or down has vertex $(0,-7)$ and passes through $(-10,18)$ . 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,-7)

and passes through

(-10,18)

. Write its equation in vertex form.

\newline

Simplify any fractions.

Vertex form of parabola: What is the vertex form of the parabola? $\newline$ Vertex form of parabola: $y = a(x - h)^2 + k$
Equation with vertex: What is the equation of a parabola with a vertex at $(0, -7)$ ? $\newline$ Substitute $0$ for $h$ and $-7$ for $k$ in vertex form. $\newline$ $y = a(x - 0)^2 + (-7)$ $\newline$ $y = ax^2 - 7$
Substitute values: $y = ax^2 - 7$ $\newline$ Replace the variables with $(-10, 18)$ in the equation. $\newline$ Substitute $-10$ for $x$ and $18$ for $y$ . $\newline$ $18 = a(-10)^2 - 7$ $\newline$ $18 = 100a - 7$
Solve for $a$ : $18 = 100a - 7$ $\newline$ Solve for $a$ . $\newline$ $18 + 7 = 100a$ $\newline$ $25 = 100a$ $\newline$ $\frac{25}{100} = a$ $\newline$ $\frac{1}{4} = a$
Equation with $a=\frac{1}{4}$ : $y = ax^2 - 7$ $\newline$ What is the equation of the parabola if $a = \frac{1}{4}$ ? $\newline$ Substitute $\frac{1}{4}$ for $a$ . $\newline$ $y = (\frac{1}{4})x^2 - 7$ $\newline$ Vertex form of parabola: $y = (\frac{1}{4})x^2 - 7$

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

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

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g(x)

g(x)

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What is the range of this quadratic function?

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Write the equation of the parabola that passes through the points

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\newline

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Find the equation of the axis of symmetry for the parabola

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Posted 4 months ago

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g(x)

g(x)

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f(x) = x^2

\newline

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a(x – h)^2 + k

a

h

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\newline

g(x) =

\newline

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x

\newline

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Write your answer in simplified, rationalized form.

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x =

\newline

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