Answer:
It is f(x) = -x^2 + 2x + 4.
Step-by-step explanation:
As it has a maximum the coefficents of x^2 will be negative.
f(x) = -x^2 + 2x + 4
The y-intercept occurs when x = 0 so
y-intercept = 0 + 0 + 4 = 4.
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ANSWER
[tex]f(x) = - {x}^{2} + 2x + 4[/tex]
EXPLANATION
The graph of the function that will have a maximum and a y-intercept of 4 is
[tex]f(x) = - {x}^{2} + 2x + 4[/tex]
To check for the y-intercept, we put x=0 into the function.
[tex]f(0) = - {0}^{2} + 2(0)+ 4[/tex]
This implies that,
[tex]f(0) = 4[/tex]
We can see that the coefficient of the quadratic term is -1.
Since the coefficient of the quadratic term is less than zero, the graph will have a maximum point.
