Question

The graph of function g is a parabola with the vertex located at (5, 9). The parabola also passes through the point (3, 1). Which of the following is an equation in vertex form for this function?

a) g(x) = 2(x - 5)² + 9
b) g(x) = 2(x - 5)² - 9
c) g(x) = 2(x - 5)² - 9
d) g(x) = "2(x + 5)²+ 9

Answer 1

The correct answer is option b. The equation in vertex form for the function is g(x) = -2(x - 5)² + 9.

Step-by-step explanation:

To determine the equation of the parabola with the vertex at (5, 9) and passing through the point (3, 1), we can use the vertex form of a parabola equation, which is g(x) = a(x - h)² + k. Where (h, k) represents the vertex of the parabola.

Plugging in the values of the vertex (5, 9), we get g(x) = a(x - 5)² + 9. Now we need to find the value of 'a'.

Using the point (3, 1) on the graph, we substitute the x and y values into the equation to solve for 'a'. This gives us the equation 1 = a(3 - 5)² + 9. Solving for 'a', we find that 'a = -2'.

Therefore, the equation in vertex form for the function is g(x) = -2(x - 5)² + 9. Option b) is the correct equation.