A parabola has its turning point at x=4 and one of the x-intercepts is x=−3.
What is the x value of the other x-intercept?
a(x-4)^2 + k = a(x+3)(x-m)
ax^2 - 8ax + 16a+k = ax^2 + a(3-m)x - 3am
m = 11
So the other root is -11
Oops -- a typo.
m = 11, not -11
Another way is --
Let the other root be m
Since the sum of the roots is -b/a
and we know that -b/2a = 4, we have -b/a = 8
8 = -3 + m
m = 11
Just realized that all that math was unnecessary. The vertex is midway between the roots.
-3 = 4-7
So the other root is at 4+7 = 11
To find the x-value of the other x-intercept of the parabola, we need to know the equation of the parabola. Specifically, we need to know the vertex form of the equation:
y = a(x-h)^2 + k
Where (h, k) represents the coordinates of the vertex and "a" is a constant that affects the shape and direction of the parabola.
Given that the turning point (vertex) of the parabola is at x=4, we know that h = 4. Additionally, we know that one of the x-intercepts is at x = -3.
In the vertex form, the x-intercepts occur where y = 0. So we can substitute x = -3 and y = 0 into the equation:
0 = a(-3-4)^2 + k
Simplifying:
0 = 49a + k
Now, we need additional information to solve for the value of "a" or "k." This could include the y-coordinate of the vertex or another point on the parabola. Without this information, we cannot determine the exact value of the other x-intercept.
Therefore, without more details or the complete equation of the parabola, we cannot determine the x-value of the other x-intercept.