The complete question is as follows:
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What is the y-intercept of the quadratic function
f(x) = (x – 6)(x – 2)?
(0,–6)
(0,12)
(–8,0)
(2,0)
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The quadratic function in standard form can be written as follows:
[tex]f(x)=ax^2+bx+c[/tex]
If we set [tex]x=0[/tex] we get the y-intercept:
[tex]f(0)=a(0)^2+b(0)+c \\ \\ c=f(0)[/tex]
In other words, the y-intercept is the point:
[tex](0,c)[/tex]
Our quadratic function is given by the form:
[tex]f(x) = (x-6)(x-2) \\ \\ \\ If \ x=0: \\ \\ f(0)=(0-6)(0-2) \\ f(0)=(-6)(-2) \\ \\ c=f(0)=12[/tex]
So the y-intercept is the point:
[tex]\boxed{(0,12)}[/tex]
Finally, the y-intercept is the point (0,12)
The axis of symmetry can be found if we know the vertex of the parabola. The x-coordinate of the vertex of the parabola can be found as:
[tex]x=-\frac{b}{2a} \\ \\ Where: \\ \\ f(x)=ax^2+bx+c \\ \\ From \ f(x) = (x-6)(x-2). \\ \\ Applying \ Distributive \ Property: \\ \\ f(x) = x^2-2x-6x+12 \\ \\ f(x) = x^2-8x+12 \\ \\ So: \\ \\ a=1 \\ b=-8 \\ c=12 \\ \\ \\ Finally: \\ \\ x=-\frac{-8}{2(1)} \\ \\ \boxed{x=4}[/tex]
Finally, the axis of symmetry is x = 4
Parabola: https://brainly.com/question/9976545
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