Consider the quadratic function f(x) = 1/5x2 – 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).
The function f(x) = 1/5x2 – 5x + 12 is a quadratic function, because the higher exponent is 2.
The correct statements are:
The value of f(-10) = 82
The graph of the function is a parabola
The graph contains the point (20,-8)
Step-by-step explanation:
The value of f(-10) = 1/5(-10)2 – 5(-10) + 12 = 1/5(100)+50+12 = 82 (<em>True</em> s<em>tatement</em>).
The graph of the function is a parabola, as all the quadratic functions. (<em>True</em> s<em>tatement).</em>
The graph of the function opens down: The parabola opens up or down depending on the "a". It is the important part of the function that determines whether it opens up or down, the parabola will open up when "a" is greater than zero.
When "a" is smaller than zero the parabola will open down. In our example a = 1/5 (greater than zero, so the parabola opens up). <em>(False Statement)</em>
The graph contains the point (20,-8). For f(20) = 1/5(20)2 - 5(20) +12 = 1/5(400) - 100 + 12 = 80 - 100 + 12 = -8 <em>(True Statement).</em>
The graph contains the point (0,0). For f(0) = 1/5(0)2 - 5(0) + 12 = 12, the correct point is (0,12) <em>(False Statement)</em>.
