Graph h(x)=(x−2)(x−4) . use the parabola tool then choose the vertex followed by one point on the parabola.

The point of the vertex is (3, -1).

Parabola is the locus of a point that moves so that it is always the same distance from a fixed point and fixed-line. The fixed point is called the focus and the fixed line is called the directrix. And the equation will be quadratic.

Quadratic equation

Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation. The general form of the quadratic equation is ax² + bx + c.

Given

h(x)=(x−2)(x−4) is equation of parabola.

The point of the vertex.

h(x)=(x−2)(x−4)

simplify the equation

h(x) = x² - 6x + 8

Then add and subtract 9.

h(x) = x² - 6x + 9 - 9 + 8

h(x) = (x -3)² -1

Then the point of the vertex is (3, -1).

More about the parabola link is given below.

link

Graph h(x)=(x−2)(x−4) is a parabola with vertex (3,-1) and the points on the parabola are (2,0) and (4,0).

Step-by-step explanation:

clearly the graph of the equation of the given function: h(x)=(x−2)(x−4) is a upward parabola whose vertex is (3,-1).

the graph of the function h(x) is attached to the answer.

The points on the parabola are: (2,0), (4,0)  which are also the x-intercepts of the graph.

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