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 statement that is true about the quadratic function is (b) the graph of the function is a parabola.

How to determine the true statements?

The quadratic function is given as

f(x) = x2 – 5x + 12

Rewrite as

f(x) = x² – 5x + 12

All quadratic functions are parabola

This means that option (b) is true

Set x = -10 to calculate f(-10)

So, we have

f(-10) = (-10)² – 5(-10) + 12

Evaluate

f(-10) = 162

This means that option (a) is false

Set x = 20 to calculate f(20)

So, we have

f(20) = (20)² – 5(20) + 12

Evaluate

f(20) = 312

This means that option (d) is false

Set x = 0 to calculate f(0)

So, we have

f(0) = (0)² – 5(2) + 12

Evaluate

f(0) = 12

This means that option (e) is false

The leading coefficient in f(x) = x² – 5x + 12 is positive

Graphs with positive leading coefficient opens up

This means that option (c) is false

Hence, the true statement about the quadratic function is (b)

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