Find the x and y Intercepts f(x)=x^2+10x+25

$f (x) = x^{2} + 10 x + 25$

Step 1

Find the x-intercepts.

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

$0 = x^{2} + 10 x + 25$

Solve the equation.

Rewrite the equation as $x^{2} + 10 x + 25 = 0$ .

$x^{2} + 10 x + 25 = 0$

Factor using the perfect square rule.

Rewrite $25$ as $5^{2}$ .

$x^{2} + 10 x + 5^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 x = 2 \cdot x \cdot 5$

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 5 + 5^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 5$ .

${(x + 5)}^{2} = 0$

Set the $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

x-intercept(s) in point form.

x-intercept(s): $(- 5, 0)$

Step 2

Find the y-intercepts.

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

$y = {(0)}^{2} + 10 (0) + 25$

Solve the equation.

Remove parentheses.

$y = 0^{2} + 10 (0) + 25$

Remove parentheses.

$y = {(0)}^{2} + 10 (0) + 25$

Simplify ${(0)}^{2} + 10 (0) + 25$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = 0 + 10 (0) + 25$

Multiply $10$ by $0$ .

$y = 0 + 0 + 25$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 25$

Add $0$ and $25$ .

$y = 25$

y-intercept(s) in point form.

y-intercept(s): $(0, 25)$

Step 3

List the intersections.

x-intercept(s): $(- 5, 0)$

y-intercept(s): $(0, 25)$

Step 4

Find the x and y Intercepts f(x)=x^2+10x+25

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