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A parabola opening up or down has vertex $(0,0)$ and passes through $(-20,20)$ . 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

(0,0)

and passes through

(-20,20)

. Write its equation in vertex form.

\newline

Simplify any fractions.

Vertex Form of Parabola: What is the vertex form of the parabola? $\newline$ The vertex form of a parabola is given by the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Equation with Vertex at ( $0$ , $0$ ): What is the equation of a parabola with a vertex at $(0, 0)$ ? $\newline$ Since the vertex is at the origin $(0, 0)$ , we substitute $h = 0$ and $k = 0$ into the vertex form equation. $\newline$ $y = a(x - 0)^2 + 0$ $\newline$ $y = ax^2$
Value of 'a' Calculation: Determine the value of 'a' using the point $(-20, 20)$ that lies on the parabola. $\newline$ We substitute $x = -20$ and $y = 20$ into the equation $y = ax^2$ to find the value of 'a'. $\newline$ $20 = a(-20)^2$ $\newline$ $20 = 400a$
Solve for 'a': Solve for 'a'. $\newline$ Divide both sides of the equation by $400$ to solve for 'a'. $\newline$ $\frac{20}{400} = a$ $\newline$ $\frac{1}{20} = a$
Final Equation in Vertex Form: Write the final equation of the parabola in vertex form. $\newline$ Now that we have the value of $a$ , we can write the equation of the parabola as: $\newline$ $y = \frac{1}{20}x^2$

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)

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Write the equation of the parabola that passes through the points

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\newline

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g(x)

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\newline

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a(x – h)^2 + k

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h

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\newline

g(x) =

\newline

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x

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