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agasfer [191]
3 years ago
14

Find the equation of a parabola with a vertical axis and its vertex at the origin and passing through the point (-2, 3)

Mathematics
1 answer:
vredina [299]3 years ago
8 0

a vertical axis, I assume it means a vertical axis of symmetry, thus it'd be a vertical parabola, like the one in the picture below.

\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \qquad \leftarrow vertical\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies y=a(x-0)^2+0 \\\\\\ \textit{we also know that } \begin{cases} x=-2\\ y=3 \end{cases}\implies 3=a(-2-0)^2+0\implies 3=4a \\\\\\ \cfrac{3}{4}=a~\hspace{10em}y=\cfrac{3}{4}(x-0)^2+0\implies \boxed{y=\cfrac{3}{4}x^2}

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Answer:

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Step-by-step explanation:

Let's do the multiplication AB.

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2 years ago
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Answer:

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Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

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Step  2  :

Equation at the end of step  2  :

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Step  3  :

Step  4  :

Pulling out like terms :

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Equation at the end of step  4  :

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Step  5  :

Equations which are never true :

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This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

5.2      Solve  :    x-2 = 0

Add  2  to both sides of the equation :

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One solution was found :

                  x = 2

Processing ends successfully

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Problem 1

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---------------

Work Shown:

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==============================================

Problem 2

<h3>Answers: c = 1 or c = -2/3</h3>

-----------------------

Work Shown:

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