Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as Micah's workings is not attached. So, there's no way to determine where Micah's error is.
However, I'll solve for the vertex of the given function.
Given
[tex]y = -9.5x^2 + 47.5x + 63[/tex]
Vertex, V is of the form:
[tex]V= (h,k)[/tex]
Where
[tex]h = -\frac{b}{2a}[/tex]
and
[tex]k = f(h)[/tex]
Solving for h:
[tex]y = -9.5x^2 + 47.5x + 63[/tex]
[tex]y = ax^2 + bx + c[/tex]
So:
[tex]a = -9.5[/tex]
[tex]b = 47.5[/tex]
[tex]c = 63[/tex]
[tex]h = -\frac{b}{2a}[/tex]
[tex]h = -\frac{47.5}{2 * -9.5}[/tex]
[tex]h = -\frac{47.5}{-19}[/tex]
[tex]h = \frac{47.5}{19}[/tex]
[tex]h = 2.5[/tex]
Solving for k
[tex]k = f(h)[/tex]
[tex]k = f(2.5)[/tex]
Substitute 2.5 for x in [tex]y = -9.5x^2 + 47.5x + 63[/tex]
[tex]k = -9.5 * 2.5^2 + 47.5* 2.5 + 63[/tex]
[tex]k = -59.375+ 118.75 + 63[/tex]
[tex]k = 122.375[/tex]
Hence:
The vertex is
[tex]V = (2.5,122.375)[/tex]
