Question

Find the x–intercepts of x2 + 8x + 15 = y.

Answer 1

The x-intercepts are (-3,0) and (-5,0).

Explanation:

We have given a equation.

x² + 8x + 15 = y

We have to find the x-intercept of the equation.

x-intercept of the equation is a point where the value of y is zero.

Putting y = 0 in given equation, we have

x²+8x+15 = 0

Factoring above equation, we have

x²+5x+3x+15 = 0

Making groups and taking common,we have

x(x+5)+3(x+5) = 0

(x+3)(x+5) = 0

Applying Zero-Product Property to above equation, we have

x+3 = 0 or x +5 = 0

x = -3 or x = -5

Hence, the x-intercepts are (-3,0) and (-5,0).

Answer 2

Hello!

The answer is: x intercepts at -3 and -5.

Why?

To find the x-intercepts we just need to find where the function tends to 0,

So,

`x^(2)+8x+15=0`

`a=1\\b=8\\c=15`

We can solve this quadratic equation by finding two numbers which its sum give as result 8 and multiplied each other gives as result 15, that numbers would be 3 and 5, knowing that we can rewrite the quadratic equation by the following way:

`x^(2) + 8x + 15= (x+3)*(x+5)`

For the new equation, we just need to find the values of x that make it 0,

When x is -3

`(-3+3)*(-3+5)=0*-2=0`

When x is -5

`(-5+3)*(-5+5)=-2*0=0`

So, the intercepts of the given function are: -3 and -5

We can also find the x-intercepts using the quadractic formula:

`\frac{-b+-\sqrt{b^(2) -4*a*c}}{2a}`

By substituting we have:

`\frac{-8+-\sqrt{8^(2) -4*1*15}}{2*1}=(-8+-√(64-60))/(2)=(-8+-√(4))/(2)=(-8+-2)/(2) \\\\x1=(-8+2)/(2)=-3\\\\x2=(-8-2)/(2)=-5`

So, the x- intercepts of the given function are: -3 and -5

Have a nice day!