Algebra Examples

y = 5 {(x - 3)}^{2} + 4

$y = 5 {(x - 3)}^{2} + 4$

Step 1

Use the vertex form,

y = a {(x - h)}^{2} + k

$y = a {(x - h)}^{2} + k$ , to determine the values of

a

$a$ ,

h

$h$ , and

k

$k$ .

a = 5

$a = 5$

h = 3

$h = 3$

k = 4

$k = 4$

Step 2

Find the vertex

(h, k)

$(h, k)$ .

(3, 4)

$(3, 4)$

Step 3

Find

p

$p$ , the distance from the vertex to the focus.

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Step 3.1

Find the distance from the vertex to a focus of the parabola by using the following formula.

\frac{1}{4 a}

$\frac{1}{4 a}$

Step 3.2

Substitute the value of

a

$a$ into the formula.

\frac{1}{4 \cdot 5}

$\frac{1}{4 \cdot 5}$

Step 3.3

Multiply

4

$4$ by

5

$5$ .

\frac{1}{20}

$\frac{1}{20}$

\frac{1}{20}

$\frac{1}{20}$

Step 4

Find the focus.

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Step 4.1

The focus of a parabola can be found by adding

p

$p$ to the y-coordinate

k

$k$ if the parabola opens up or down.

(h, k + p)

$(h, k + p)$

Step 4.2

Substitute the known values of

h

$h$ ,

p

$p$ , and

k

$k$ into the formula and simplify.

(3, \frac{81}{20})

$(3, \frac{81}{20})$

(3, \frac{81}{20})

$(3, \frac{81}{20})$

Step 5