Answer:
49
Step-by-step explanation:
Because there is a minus sign infront of x-3, we can convert x-3 into the negative form:
- * x
- * -3
-x + 3
Which gives us:
(-x + 3)(x + 11)
Now expand the brackets with the formula:
(a + b)(c + d) = ac + ad + bc + bd
-x * x = -x²
-x * 11 = -11x
3 * x = 3x
3 * 11 = 33
-x² - 11x + 3x + 33
-x² - 8x + 33
The formula for finding the x coordinate of a vertex in a quadratic equation is:
x = [tex]\frac{-b}{2a}[/tex]
Plug known variables in:
[tex]x = \frac{-(-8)}{2(-1)}[/tex]
[tex]x = \frac{8}{-2}[/tex]
[tex]x = -4[/tex]
Now, to find the y coordinate, plug this variable back into the quadratic equation:
-x² - 8x + 33
[tex]y = -(-4^2) - (32) + 33\\y = -16 + 32 + 33\\\\[/tex]
y = 49
So the y coordinate of the vertex is 49.
Hope this helps!
