Question

Find the x-intercepts for the parabola defined by the equation below. y = x2 + 9x + 14

A. (-2, 0) and (-7, 0)


B. (9, 0) and (14, 0)



C. (0, -2) and (0, -7)


D. (0, 9) and (0, 14)

Answer 1

x - intercepts are (-7,0) and (-2,0)

A is the correct option.

Explanation:

We have been given the equation of the parabola
`y=x^2+9x+14`

For x- intercept, y = 0

`0=x^2+9x+14`

We can split the middle term as 9x = 7x +2x

`x^2+7x+2x+14=0`

Now take GCF

`x(x+7)+2(x+7)=0`

Factored out the common term

`(x+7)(x+2)=0`

Apply the zero product property

`(x+7)=0,(x+2)=0`

Solve for x

`x=-7,-2`

Hence, x - intercepts are (-7,0) and (-2,0)

A is the correct option.