Question

Consider the quadratic function f(x)=x²-5x+12. Which statements are true about the function and its
graph? Select three options.

A. The value of f(-10) = 82
B. The graph of the function is a parabola.
C. The graph of the function opens down.
D. The graph contains the point (20,-8).
E. The graph contains the point (0, 0).

1. phucdien
There is only one statement that is true: B. The graph of the function is a parabola.

### How to study and interpret the characteristics of quadratic equations

In this question we have a quadratic equation, whose characteristics have to be inferred and analyzed. We need to prove each of the five choices presented in the statement:
Choice A:
If we know that x = – 10, then we evaluated it at the function:
f(- 10) = (- 10)² – 5 · (- 10) + 12
f(- 10) = 162
False
Choice B:
By analytical geometry we know that all functions of the form y = a · x² + b · x + c always represent parabolae.
True
Choice C:
The quadratic function opens up as its leading coefficient is greater that 0.
False
Choice D:
If we know that x = 20, then we evaluate it at the function:
f(20) = 20² – 5 · (20) + 12
f(20) = 312
False
Choice E:
If we know that x = 0, then we evaluate it at the function:
f(0) = 0² – 5 · (0) + 12
f(0) = 12
There is only one statement that is true: B. The graph of the function is a parabola.