Question

A parabola with its vertex at (24,10) and its axis of symmetry parallel to the y-axis passes through point (4,290). Write an equation of the

parabola. Then find the value of y when x = 34.

Answer 1

The equation of the parabola is y = 0.7(x - 24)^2 + 10. When x = 34, y = 80.

Step-by-step explanation:

To write the equation of a parabola, we need to determine the values of a, b, and c. Given that the parabola has its vertex at (24, 10), we can use the vertex form of a parabola equation, which is y = a(x - h)^2 + k, where (h, k) represents the vertex. In this case, the equation becomes y = a(x - 24)^2 + 10. We can substitute the coordinates of the point (4, 290) to find the value of a. Substituting x = 4 and y = 290, we get 290 = a(4 - 24)^2 + 10. Simplifying this equation gives us 290 = 400a + 10. Solving for a gives us a = (290 - 10) / 400 = 280 / 400 = 0.7.

Therefore, the equation of the parabola is y = 0.7(x - 24)^2 + 10.

To find the value of y when x = 34, we can substitute x = 34 into the equation: y = 0.7(34 - 24)^2 + 10 = 0.7(10)^2 + 10 = 0.7(100) + 10 = 70 + 10 = 80.

Answer 2

Not executable

Step-by-step explanation:

f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)

so the equation of parabola with the vertex (24, 10) is :

f(x) = a(x - 24)² + 10

the parabola's axis of symmetry parallel to the y-axis and passing through point (4,290) means: h = 4

4 ≠ 24

That means you write something wrong in your question.