What are the x-intercepts of y=x2+2x−15?

Gerald Ritter

Gerald Ritter

Answered

2022-01-23

What are the x-intercepts of y=x2+2x15?

Answer & Explanation

Roman Stevens

Roman Stevens

Expert

2022-01-24Added 10 answers

Step 1
By setting it equal to zero,
x2+2x15=0
By factoring out,
(x+5)(x3)=0
By setting each factor equal to zero,
{x+5=0x=5x3=0x=3
Hence, the x-intercepts are: x=5, 3
porekalahr

porekalahr

Expert

2022-01-25Added 10 answers

Step 1
y=x2+2x15
Find the x-intercepts.
To find the x-intercept(s), substitute in 0 for y and solve for x.
0=x2+2x15
Solve the equation.
Rewrite the equation as
x2+2x15=0
Factor x2+2x15 using the AC, method.
Consider the form x2+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
=3, 5
Write the factored form using these integers.
(x3)(x+5)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x3=0
x+5=0
Set the first factor equal to 0 and solve.
x3=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 (x3)(x+5)=0 true.
x=3, 5
Find the y-intercepts.
To find the y-intercept(s), substitute in 0 for x and solve for y.
y=(0)2+2(0)15
Solve the equation.
Remove parentheses.
y=(0)2+2(0)15
Simplify (0)2+2(0)15
Simplify each term.
y=0+015
Simplify by adding zeros.
y=15

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