The vertex is the minimum or the maximum point of the parabola.
x and f(x) represent the horizontal and the vertical coordinates of the vertex.
The standard form of a parabola is
[tex]f(x) = ax^2 +bx + c[/tex]
The x coordinate of the parabola is calculated using:
[tex]x =-\frac{b}{2a}[/tex]
The value of the x-coordinate is then plugged in, into the equation to calculate the y-coordinate, as follows:
[tex]f(\frac{b}{2a}) = a(-\frac{b}{2a})^2 + b(-\frac{b}{2a}) + c[/tex]
At the end of the calculation,
x and f(x) represent the horizontal and the vertical coordinates of the vertex.
Take for instance:
[tex]f(x) = 2x^2 + 4x - 9[/tex]
The x-coordinate of the vertex is:
[tex]x = -\frac b{2a}[/tex]
[tex]x = -\frac 4{2 \times 2}[/tex]
[tex]x = -\frac 44[/tex]
[tex]x=-1[/tex]
The y-coordinate is:
[tex]f(x) = 2x^2 + 4x - 9[/tex]
[tex]f(-1) =2 \times (-1)^2 + 4 \times -1 - 9[/tex]
[tex]f(-1) =-11[/tex]
So, the vertex of [tex]f(x) = 2x^2 + 4x - 9[/tex] is (-1,11)
See attachment for illustration of vertex of [tex]f(x) = 2x^2 + 4x - 9[/tex]
Read more about vertex of parabola at:
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