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The graph of which function will have a maximum and a y-intercept of 4?
a. f(x) = 4x2 + 6x – 1
b. f(x) = –4x2 + 8x + 5
c. f(x) = –x2 + 2x + 4
d. f(x) = x2 + 4x – 4

Respuesta :

W0lf93
The y-intercept of the equation is the value of the variable y or in this case, f(x), when x is equated to zero. Out of all the choices presented in this item, if x is equated to zero, the first two terms will be equal to zero, leaving the third term only for the numerical value of f(x). 

From the choices presented, the answer would be f(x) = -x2 + 2x + 4. Thus, the answer is the third choice, C. 

The quadratic equation [tex](-x^2+2x+4)[/tex] have the coefficient of [tex]x^2[/tex] less than zero therefore its graph has a maximum point and it also have y-intercept equal to 4.

The quadratic equation that have the coefficient of [tex]x^2[/tex] less than zero, then the graph of that quadratic equation have a maximum point.

Therefore according to the given equation the quadratic equation that have a maximum point are: [tex](-4x^2+8x +5)\;and\;(-x^2+2x+4)[/tex].

Now, to evaluate the value of y-intercept, put the value of x equal to zero.

a). [tex]4x^2+6x-1[/tex]

put x = 0 in above equation to get the y-intercept:

[tex]4(0)^2+6(0)-1=-1[/tex]

So, the equation  [tex]4x^2+6x-1[/tex] has y-intercept -1.

b). [tex]-4x^2+8x+5[/tex]

put x = 0 in above equation to get the y-intercept:

[tex]-4(0)^2+8(0)+5=5[/tex]

So, the equation  [tex]-4x^2+8x+5[/tex] has y-intercept 5.

c). [tex]-x^2+2x+4[/tex]

put x = 0 in above equation to get the y-intercept:

[tex]-(0)^2+2(0)+4=4[/tex]

So, the equation  [tex]-x^2+2x+4[/tex]  has y-intercept 4.

d). [tex]x^2+4x-4[/tex]

put x = 0 in above equation to get the y-intercept:

[tex](0)^2+4(0)-4=-4[/tex]

So, the equation   [tex]x^2+4x-4[/tex] has y-intercept -4.

Therefore, the correct option is c).

For more information, refer the link given below:

https://brainly.com/question/11243794

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