The vertex of the parabola will be at point (1,-9).
We have existed given factored format of a quadratic equation
y = (x-4)(x+2).
We want to estimate the vertex and x-intercepts from the given equation.
We know that x-intercepts of a graph are those points at which the graph connects or crosses the x-axis and y-coordinates of x-intercepts exist consistently at zero. Substitute y=0 in the given equation to estimate the x-intercepts.
0 = (x-4)(x+2)
(x-4)=0 or (x+2) = 0
x - 4 + 4 = 0+4 or x + 2 - 2 = 0 - 2
x = 4 or x = -2
Since y-coordinates of x-intercepts will be 0, therefore, x-intercepts of the graph will be (4,0),(-2,0).
To estimate the vertex of the parabola, we will extend the given expression utilizing FOIL.
(x-4)(x+2)
[tex]x * x+x * 2-4 * x-4 * 2[/tex]
[tex]x^{2}+2 x-4 x-8[/tex]
[tex]x^{2}-2 x-8[/tex]
We will use formula [tex]$\frac{-b}{2 a}$[/tex] to estimate the x-coordinate of vertex of parabola, where, a and b denotes the coefficient of [tex]$x^{2}$[/tex] and x respectively.
x-coordinate of vertex [tex]$=\frac{-(-2)}{2 * 1}$[/tex]
x-coordinate of vertex [tex]$=\frac{2}{2}=1$[/tex]
Substitute x=1 in the expression to estimate the y-coordinate of parabola.
y-coordinate of vertex[tex]$=1^{2}-2 * 1-8$[/tex]
y-coordinate of vertex =1-2-8
y-coordinate of vertex = -9
The vertex of the parabola will be at point (1,-9).
Therefore, the correct answer is option C vertex (1,-9).
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