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A parabola opening up or down has vertex $(0,0)$ and passes through $(4,1)$ . Write its equation in vertex form. $\newline$ Simplify any fractions. $\newline$ ______

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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

(4,1)

. Write its equation in vertex form.

\newline

Simplify any fractions.

\newline

______

Vertex Form Explanation: What is the vertex form of the parabola? $\newline$ 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 at Origin: 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. $\newline$ $y = a(x - 0)^2 + 0$ $\newline$ $y = ax^2$
Value of 'a' Calculation: Determine the value of 'a' using the point $(4, 1)$ that lies on the parabola. $\newline$ We substitute $x = 4$ and $y = 1$ into the equation $y = ax^2$ to find 'a'. $\newline$ $1 = a(4)^2$ $\newline$ $1 = 16a$
Solving for 'a': Solve for 'a'. $\newline$ Divide both sides of the equation by $16$ to isolate 'a'. $\newline$ $a = \frac{1}{16}$
Final Parabola Equation: Write the equation of the parabola using the value of ' extit{a}'. $\newline$ Substitute $a = \frac{1}{16}$ into the equation $y = ax^2$ . $\newline$ $y = \left(\frac{1}{16}\right)x^2$ $\newline$ This is the equation of the parabola in vertex form.

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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Posted 8 months ago

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g(x)

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Question

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Posted 5 months ago

Question

Write the equation of the parabola that passes through the points

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\newline

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\newline

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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)

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f(x) = x^2

\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

\newline

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