Gerald Ritter

2022-01-23

What are the x-intercepts of $y={x}^{2}+2x-15?$

Roman Stevens

Expert

Step 1
By setting it equal to zero,
${x}^{2}+2x-15=0$
By factoring out,
$\left(x+5\right)\left(x-3\right)=0$
By setting each factor equal to zero,
$\left\{\begin{array}{c}x+5=0⇒x=-5\\ x-3=0⇒x=3\end{array}$
Hence, the x-intercepts are:

porekalahr

Expert

Step 1
$y={x}^{2}+2x-15$
Find the x-intercepts.
To find the x-intercept(s), substitute in 0 for y and solve for x.
$0={x}^{2}+2x-15$
Solve the equation.
Rewrite the equation as
${x}^{2}+2x-15=0$
Factor ${x}^{2}+2x-15$ using the AC, method.
Consider the form ${x}^{2}+bx+c$. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -15 and whose sum is 2

Write the factored form using these integers.
$\left(x-3\right)\left(x+5\right)=0$
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
$x-3=0$
$x+5=0$
Set the first factor equal to 0 and solve.
$x-3=0$
Add 3 to both sides of the equation.
$x=3$
Set the next factor equal to 0.
$x+5=0$
Subtract 5 from both sides of the equation.
$x=-5$
The final solution is all the values that make $\left(x-3\right)\left(x+5\right)=0$ true.

Find the y-intercepts.
To find the y-intercept(s), substitute in 0 for x and solve for y.
$y={\left(0\right)}^{2}+2\left(0\right)-15$
Solve the equation.
Remove parentheses.
$y={\left(0\right)}^{2}+2\left(0\right)-15$
Simplify ${\left(0\right)}^{2}+2\left(0\right)-15$
Simplify each term.
$y=0+0-15$
$y=-15$