Question

The graph of the quadratic function f(x)=ax^{2}+bx+c

intersects the y-axis at point A (0,5) and has its vertex at point B (4, 13).
Write down the value of C

Answer 1

In the quadratic function given, the value of 'c' is the y-coordinate of the point where the graph intersects the y-axis. Since the graph passes through point A (0,5), the value of 'c' is 5.

Step-by-step explanation:

The student asked for the value of c in the quadratic function f(x)=ax^2+bx+c that intersects the y-axis at point A (0,5) and has its vertex at point B (4, 13).

To find the value of c, we need to understand that the intersection with the y-axis will give us the y-intercept, which is the point where x is zero.

Since the function intersects the y-axis at point A (0,5), we can substitute x with 0 in the function and get f(0)=a*(0)^2+b*(0)+c.

Since f(0) = 5, it follows that c = 5.