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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)

Verified Answer :

SociometricStar

Answer:

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

A is the correct option.

Step-by-step 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.

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