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Find the equation of the quadratic function
g whose graph is shown below.

g(x)=

Find the equation of the quadratic function $g$ whose graph is shown below. $\newline$ $g(x)=$

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Evaluate piecewise-defined functions

Full solution

Q. Find the equation of the quadratic function

g

whose graph is shown below.

\newline

g(x)=

Identify Vertex and Points: Identify the vertex and points on the graph. Assume vertex at $(-2, 3)$ and points $(0, 7)$ and $(-4, 7)$ .
Use Vertex Form: Use vertex form of a quadratic equation, $g(x) = a(x-h)^2 + k$ , where (h, k) is the vertex. Here, h = $-2$ and k = $3$ .
Substitute Vertex: Substitute the vertex into the equation: $g(x) = a(x+2)^2 + 3$ .
Use Point to Find 'a': Use point ( $0$ , $7$ ) to find 'a'. Substitute x = $0$ and g(x) = $7$ into the equation: $7 = a(0+2)^2 + 3$ .
Solve for 'a': Solve for 'a': $7 = 4a + 3$ leads to $4a = 4$ , so $a = 1$ .
Write Final Equation: Write the final equation: $g(x) = (x+2)^2 + 3$ .

More problems from Evaluate piecewise-defined functions

Question

\vec{u}

has an initial point

(4,8)

and a terminal point

(2,4)

\newline

Find the magnitude of

\vec{u}

\newline

Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.

\newline

\|\vec{u}\|=\square

Posted 3 months ago

Question

\vec{u}

has an initial point

(5,1)

and a terminal point

(-3,4)

\newline

Find the magnitude of

\vec{u}

\newline

Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.

\newline

\|\vec{u}\|=\square

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Question

Rewrite the expression in the form

x^{n}

\newline

Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).

\newline

\sqrt{x^{\frac{3}{4}} x^{-1}}=\square

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Question

a

. Express your answer as a proper or improper fraction in simplest terms.

\newline

-\frac{5}{6}-\frac{1}{5} a=-\frac{5}{8}

\newline

a=

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Find the value of

x

in the equation below.

\newline

\frac{x}{7}=8

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x=

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Find the value of

x

in the equation below.

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\frac{x}{9}=8

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Given the function

y=\frac{\sqrt[5]{x^{6}}}{3}

\frac{d y}{d x}

. Express your answer in radical form without using negative exponents, simplifying all fractions.

\newline

\frac{d y}{d x}=

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Question

Given the function

f(x)=\frac{1}{\sqrt[4]{x^{3}}}

f^{\prime}(x)

. Express your answer in radical form without using negative exponents, simplifying all fractions.

\newline

f^{\prime}(x)=

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Solve the following equation for

a

. Be sure to take into account whether a letter is capitalized or not.

\newline

\frac{a}{D}=7

\newline

a=

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Solve the following equation for

A

. Be sure to take into account whether a letter is capitalized or not.

\newline

\frac{A}{g}=m

\newline

A=

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