483 views
4 votes
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

1 Answer

2 votes

Final answer:

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.

User David Pilkington
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories