Consider the quadratic equation y=x 2 +12x+35. Find the x−intercepts of the graph of the quadratic relationship.

To find the x-intercepts of the graph of the quadratic equation y = x^2 + 12x + 35, we need to set y to 0 and solve for x.

Step 1: Set y to 0 0 = x^2 + 12x + 35

Step 2: Solve for x This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve for x using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / 2a.

In this equation, a = 1, b = 12, and c = 35.

Step 3: Substitute a, b, and c into the quadratic formula x = [-12 ± sqrt((12)^2 - 4135)] / 2*1 x = [-12 ± sqrt(144 - 140)] / 2 x = [-12 ± sqrt(4)] / 2 x = [-12 ± 2] / 2

Step 4: Solve for x x = [-12 + 2] / 2 = -10 / 2 = -5 x = [-12 - 2] / 2 = -14 / 2 = -7

So, the x-intercepts of the graph of the quadratic equation y = x^2 + 12x + 35 are x = -5 and x = -7.