Question

1. find the zero(s) of the quadratic equation by factoring. (factor the following quadratic and solve for x)

$x^{2}+6x + 9 = 0$
○ x = 3
○ x = -3
○ x = {-3, 3}

1. if you factor a quadratic equation, and you get 1 solution, that means that the graph of that function would intercept the x-axis

○ 1 time
○ 2 times
○ never

Explanation:

Step1: Factor the quadratic equation

The quadratic equation \(x^{2}+6x + 9=0\) can be factored using the formula \((a + b)^{2}=a^{2}+2ab + b^{2}\). Here \(a=x\) and \(b = 3\) since \(x^{2}+6x+9=(x + 3)^{2}\). So the equation becomes \((x + 3)^{2}=0\).

Step2: Solve for \(x\)

Set \((x + 3)^{2}=0\). Taking the square root of both sides, we get \(x+3=0\). Solving for \(x\) gives \(x=-3\).

For the second question, the number of solutions of a quadratic equation (found by factoring) is equal to the number of times the graph of the quadratic function (since \(y=x^{2}+6x + 9\) is a function) intersects the \(x\) - axis. If there is 1 solution (a repeated root), the graph touches the \(x\) - axis at exactly 1 point.

Answer:

1. \(x=-3\)
2. 1 time