82.1k views
5 votes
You have a parabola. The x-intercept is (8,0), the y-intercept is (0,0), and the vertex is (4,-3). What is the equation of the parabola?

A) y = (x - 4)^2 - 3
B) y = (x + 4)^2 - 3
C) y = -(x - 4)^2 - 3
D) y = -(x + 4)^2 - 3

User Don Gorgon
by
7.7k points

1 Answer

5 votes

Final answer:

The correct equation of the parabola with the given x-intercept, y-intercept, and vertex is Option A: y = (x - 4)^2 - 3. The value of 'a' is found by substituting the x-intercept into the vertex form of the equation, yielding a positive coefficient and an upward-facing parabola.

Step-by-step explanation:

The equation of a parabola with a vertex at (4, -3) and the symmetry axis being vertical can be written in the form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Since the vertex is given as (4, -3), we substitute h and k to get the equation y = a(x - 4)^2 - 3. Now, given that one x-intercept is at (8, 0), we can plug these values into our equation to find the value of a. We get:

0 = a(8 - 4)^2 - 3

0 = 16a - 3

16a = 3

a = 3/16

Because the coefficient a is positive, the parabola opens upwards, and since it includes the y-intercept (0,0), the equation could not have a negative coefficient before the squared term, as it would not cross the y-axis there.

Thus, the correct equation of the parabola is Option A: y = (x - 4)^2 - 3, which can be written as y = (3/16)(x - 4)^2 - 3 when the value of 'a' is included.

User Cornelius Qualley
by
8.9k 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