Algebra Examples

$f (x) = 4 {(x - 3)}^{2}$

To find the x-intercept, substitute in $0$ for $y$ and solve for $x$ .

$0 = 4 {(x - 3)}^{2}$

Solve the equation.

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Rewrite the equation as $4 {(x - 3)}^{2} = 0$ .

$4 {(x - 3)}^{2} = 0$

Divide both sides of the equation by $4$ . Dividing $0$ by any non-zero number is $0$ .

${(x - 3)}^{2} = 0$

Set $x - 3$ equal to $0$ and solve for $x$ .

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Set the factor equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The solution is the result of $x - 3 = 0$ .

$x = 3$

To find the y-intercept, substitute in $0$ for $x$ and solve for $y$ .

$y = 4 {((0) - 3)}^{2}$

Solve the equation.

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Remove the extra parentheses.

$y = 4 {(0 - 3)}^{2}$

Simplify $4 {(0 - 3)}^{2}$ .

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Subtract $3$ from $0$ .

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

Raise $- 3$ to the power of $2$ .

$y = 4 \cdot 9$

Multiply $4$ by $9$ .

$y = 36$

These are the $x$ and $y$ intercepts of the equation $y = 4 {(x - 3)}^{2}$ .

x-intercept: $(3, 0)$

y-intercept: $(0, 36)$

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