Question

A parabola intersects the x-axis at x = 3 and x = 9.

Answer 1

Answer:

The x-coordinate of the parabola's vertex is 6.

Step-by-step explanation:

A parabola in the following format:

$y = ax^{2} + bx + c$

With

$\Delta = b^{2} - 4ac$

Has the following vertex:

$V = (x_{v}, y_{v})$

In which

$x_{v} = -\frac{b}{2a}$

$y_{v} = -\frac{\Delta}{4a}$

In this problem, we have that:

A parabola intersects the x-axis at x = 3 and x = 9. This means that the roots are x = 3 and x = 9, and that our parabola is defined by the following equation:

$y = (x - 3)(x - 9) = x^{2} - 12x + 27$

So

$x = 1, b = -12, c = 27$

$x_{v} = -\frac{b}{2a} = -\frac{-12}{2} = 6$

The x-coordinate of the parabola's vertex is 6.

Answer 2

Answer:

6

Step-by-step explanation:

This function corresponds to 'even' function, then

in order to calculate the 'x' of the vertex: (3+9)/2=6.