Question

A quadratic function has these characteristics: x = 2 is the equation for the axis of symmetry, x = 4 is an x-intercept, y = 8 is the maximum value. Determine, algebraically, the exact value of the y-intercept of this parabola.

A. y = 0
B. y = 8
C. y = 16
D. y = -8

Answer 1

To determine the y-intercept of the parabola, we need to find the value of y when x = 0. The exact value of the y-intercept is y = -8.

Step-by-step explanation:

To determine the y-intercept of the parabola, we need to find the value of y when x = 0. Since the equation for the axis of symmetry is x = 2, the x-coordinate of the vertex is 2. Since x = 4 is an x-intercept, the parabola intersects the x-axis at (4,0). We can use this information to find the equation of the parabola in the form y = ax^2 + bx + c. Plugging in the values (2, 8) and (4, 0) into the equation, we can solve for a, b, and c. Once we have the equation, we can substitute x = 0 to find the y-intercept.

So, the exact value of the y-intercept is y = -8.