Question

Jasmine used factoring and completing the square to analyze this quadratic function, as shown. f(x) = 22 + 8x + 12 = (x+6)(x + 2) f(x) = x^2 + 8x + 12 = 22 + 8x + 16 - 4 = (x +4)² - 4 What are the zeros, the vertex, and the line of symmetry of the graph of f(x)?

a) Zeros: -6, -2; Vertex: (-4, -4); Line of symmetry: x = -4
b) Zeros: -4, 4; Vertex: (-2, 4); Line of symmetry: x = -2
c) Zeros: -2, 6; Vertex: (-4, -4); Line of symmetry: x = -4
d) Zeros: -6, 2; Vertex: (-4, -4); Line of symmetry: x = -4

Answer 1

The zeros of the quadratic function are -6 and -2, the vertex is (-4, -4), and the line of symmetry is x = -4.

Step-by-step explanation:

The zeros of the graph of the quadratic function f(x) = x^2 + 8x + 12 are the x-values that make the function equal to zero. To find the zeros, we set the function equal to zero and solve for x. From the factored form of the function (x+6)(x+2) = 0, we can see that the zeros are -6 and -2.

The vertex of a quadratic function is the highest or lowest point on the graph. To find the vertex, we use the formula x = -b / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 8, and c = 12. Substituting these values into the formula, we get x = -8 / (2 * 1) = -4. The y-value of the vertex can be found by substituting the x-value into the original function: f(-4) = (-4)^2 + 8(-4) + 12 = 16 - 32 + 12 = -4. So, the vertex is (-4, -4).

The line of symmetry of a quadratic function is a vertical line that passes through the vertex. In this case, the line of symmetry is x = -4.