Question

Three equations that all represent the same function are shown. Select the equation that includes the zeros of

f(x) as numbers that appear in the equation.
a) f(x)=−2x²+24x−54
b) f(x)=−2(x−3)(x−9)
c) f(x)=−2(x+6)²+18
equation that represents the zero is: (type the letter only)

Which of the equations represents the vertex: (type the letter only)

What is the axis of symmetry: (type your answer, no space)

The parabola has (maximum/minimum) value of: (type your answer)

Answer 1

Equation (b) includes the zeros of the function within it, as it is in factored form. Equation (c) represents the vertex, being in vertex form. The parabola's axis of symmetry is x = -6 and since the parabola opens downwards, it has a maximum value.

Step-by-step explanation:

To determine the equation that includes the zeros of the function f(x), we should look for the equation in factored form, as the factors directly reveal the zeros. The factored form of a quadratic equation is f(x) = a(x - r)(x - s), where r and s represent the zeros. In this case, equation (b) f(x) = -2(x - 3)(x - 9) represents the zeros as 3 and 9.

The equation that represents the vertex form is where the equation is in the format f(x) = a(x - h)² + k, with (h, k) being the vertex's coordinates. For these given equations, (c) f(x) = -2(x + 6)² + 18 is in the vertex form, which means it represents the vertex of the parabola.

The axis of symmetry for a parabola in vertex form, f(x) = a(x - h)² + k, is x = h. Referring to equation (c) again, the axis of symmetry is x = -6.

Since the coefficient of the x² term in the equations is negative (a = -2), the parabola opens downwards, which means it has a maximum value at the vertex.