+618 The graph of the quadratic $y = ax^2 + bx + c$ has the following properties: (1) The maximum value of $y = ax^2 + bx + c$ is 5, which occurs at $x = 3$. (2) The graph passes through the point $(0,-13)$. If the graph passes through the point $(4,m)$, then what is the value of $m$?
+23246 If the x-value of the vertex (maximum value) is 3 and the y-value is 5, the vertex occurs at (3, 5).
An equation for a parabola is: y - k = a(h - h)2 [ The vertex occurs at (h, k) ]
---> y - 5 = a(x - 3)2
Since the graph passes through the point (0, -13), we have:
-13 - 5 = a(0 - 3)2
- 18 = a(-3)2
-18 = a·9
a = -2
So, the equation is: y - 5 = -2(x - 3)2
For the point (4, m), x = 4 and y = m ---> m - 5 = -2(4 - 3)2
Now, solve this for m.
+23246 If the x-value of the vertex (maximum value) is 3 and the y-value is 5, the vertex occurs at (3, 5).
An equation for a parabola is: y - k = a(h - h)2 [ The vertex occurs at (h, k) ]
---> y - 5 = a(x - 3)2
Since the graph passes through the point (0, -13), we have:
-13 - 5 = a(0 - 3)2
- 18 = a(-3)2
-18 = a·9
a = -2
So, the equation is: y - 5 = -2(x - 3)2
For the point (4, m), x = 4 and y = m ---> m - 5 = -2(4 - 3)2
Now, solve this for m.
