Question

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

Answer 1

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).

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.

Answer 2

To graph the function h(x) = (x-2)(x-4), we can use the parabola tool to plot the vertex and one point on the parabola. The function is a quadratic function in standard form, f(x) = ax^2 + bx + c, where a = 1, b = -6, and c = 8.

To find the vertex, we can use the formula x = -b/2a. Substituting the values, we get x = -(-6)/(2*1) = 3. The y-coordinate of the vertex can be found by substituting x = 3 into the function, giving us h(3) = (3-2)(3-4) = -1. Therefore, the vertex is (3, -1).

To find another point on the parabola, we can choose any value of x and evaluate the function. For example, if we let x = 0, we get h(0) = (0-2)(0-4) = 8. Therefore, the point (0, 8) is on the parabola.

Using the parabola tool, we can plot the vertex at (3, -1) and the point (0, 8) to graph the function h(x) = (x-2)(x-4).