Question

Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).

A. y = -3x^2 + 12x
B. y = 3x^2 - 12x
C. y = 3x^2 + 12x
D. y = -3x^2 - 12x

Answer 1

No answer set meets the given requirements.

Step-by-step explanation:

None of the answer options meet the two criteria of a (2,0) vertex and a (0,12) y-intercept. Also A. and B. and identical to C. and D.

Just looking at the requirement of (0,12), we can find a problem. None of the equations would produce a value of 12 for y when x = 0. There is no constant term: All values depend on x. So when x = 0, y must also = 0, not 12.

See how the attached graph could be used to identify the equation with a vertx at (2,0) and y-0ntercept at (0,12). Review the problem and graph the changes, as appropriate.

Answer 2

To find the equation of the parabola, use the vertex form y = a(x - h)^2 + k. Substitute the given vertex and y-intercept to solve for a. The correct equation is y = -3x^2 + 12x.

Step-by-step explanation:

To find the equation of the parabola, we need to use the vertex form of a parabola, which is y = a(x - h)^2 + k, where (h, k) is the vertex.

We are given that the vertex is (2, 0), so the equation becomes y = a(x - 2)^2 + 0.

We also know that the y-intercept is (0, 12), so when x=0, y=12. Substituting these values into the equation, we can solve for a.
When x=0, y=12:

12 = a(0 - 2)^2 + 0
Simplifying and solving for a, we get a = -3.
Therefore, the equation of the parabola is y = -3(x - 2)^2 + 0, which simplifies to y = -3x^2 + 12x - 12. Hence, the correct answer is option A: y = -3x^2 + 12x.