Question

What is the rule for finding the vertex of a formula in Standard form? Use that rule to

Answer 1

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

$f(x) = ax^2 +bx + c$

The x coordinate of the parabola is calculated using:

$x =-\frac{b}{2a}$

The value of the x-coordinate is then plugged in, into the equation to calculate the y-coordinate, as follows:

$f(\frac{b}{2a}) = a(-\frac{b}{2a})^2 + b(-\frac{b}{2a}) + c$

At the end of the calculation,

x and f(x) represent the horizontal and the vertical coordinates of the vertex.

Take for instance:

$f(x) = 2x^2 + 4x - 9$

The x-coordinate of the vertex is:

$x = -\frac b{2a}$

$x = -\frac 4{2 \times 2}$

$x = -\frac 44$

$x=-1$

The y-coordinate is:

$f(x) = 2x^2 + 4x - 9$

$f(-1) =2 \times (-1)^2 + 4 \times -1 - 9$

$f(-1) =-11$

So, the vertex of $f(x) = 2x^2 + 4x - 9$ is (-1,11)

See attachment for illustration of vertex of $f(x) = 2x^2 + 4x - 9$

Read more about vertex of parabola at:

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