Question

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Answer 1

The statements that are true about the quadratic function and its graph include the following:

• The value of f(–10) = 82
• The graph of the function is a parabola.
• The graph contains the point (20, –8).

How to determine the true statements about this function and its graph?

In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.

Next, we would determine the statements about the quadratic function and its graph that are true:

At point (-10, 82), we have:

`f(x) = (1)/(5) \ x^2 - 5x + 12`

`f(x) = x^2/5 - 5x + 12`

`f(-10) = -10^2/5 - 5(-10) + 12`

`f(-10) = 82`

At point (20, -8), we have:

`f(x) = (1)/(5) \ x^2 - 5x + 12`

`f(x) = x^2/5 - 5x + 12`

`f(20) = 20^2/5 - 5(20) + 12`

`f(20) = -8`

In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.