Question

Part A: Show all work to solve the quadratic equation x2 − 12x + 35 = 0 by factoring.Part B: Using complete sentences, explain what the solutions from Part A represent on the graph.

Answer 1

Answer:

A) Notice that:

$\begin{gathered} x^2-12x+35=x^2+(-5-7)x+(-5)(-7) \\ =x^2-5x-7x+(-5)(-7)=x(x-5)-7(x-5) \\ =(x-7)(x-5)\text{.} \end{gathered}$

Therefore:

$x^2-12x+35=0\text{ if and only if x=7 or x=5.}$

B) The solutions from part A represent the x-coordinates of the x-intercepts of the graph of the function

$f(x)=x^2-12x+35.$