Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function.
-$$f ( x ) = x ^ { 2 } - 14 x + 24$$
A) $x = 22 , x = 2$
B) $x = - 12 , x = - 2$
C) $x = \sqrt { 5 } , x = - 1$
D) $x = 12 , x = 2$

Question

Quizplus · Accepted Answer

To find the zeros of the quadratic function $f(x) = x^2 - 14x + 24$, we complete the square. First, we rewrite the function in the form $x^2 - 14x = -24$. To complete the square, we add and subtract $\left(\frac{-14}{2}\right)^2 = 49$ inside the equation, leading to $x^2 - 14x + 49 = 25$, which simplifies to $(x - 7)^2 = 25$. Taking the square root of both sides gives $x - 7 = \pm 5$, so $x = 12$ or $x = 2$, which are the x-intercepts of the graph.

Find the Zeros of the Quadratic Function by Completing the Square