Final answer:
Among the statements about the function f(x) = x² - 5x + 12, it is true that the graph is a parabola, but it opens upwards, not downwards, and the function does not contain the points (20, -8) or (0, 0).
Step-by-step explanation:
When considering the quadratic function f(x) = x² - 5x + 12, there are several properties we can analyze to determine which statements are true about the function and its graph.
First, let's calculate the value of f(-10). By plugging in -10 for x, we get:
f(-10) = (-10)² - 5(-10) + 12 = 100 + 50 + 12 = 162.
So, the statement 'The value of f(-10) = 82' is incorrect.
The graph of the function is determined by the general shape of the equation, which is a quadratic. Quadratics are known for their characteristic parabolic shapes. Thus, the statement 'The graph of the function is a parabola' is true.
Since the coefficient of the x² term is positive, the graph opens upwards. This contradicts the statement 'The graph of the function opens down.'
To check if the graph contains the point (20, -8), we can substitute x = 20 into the equation and see if -8 is the result:
f(20) = (20)² - 5(20) + 12 = 400 - 100 + 12 = 312.
Therefore, the graph does not contain the point (20, -8).
The last statement to validate is 'The graph contains the point (0, 0)'. To check this, we can substitute x = 0:
f(0) = (0)² - 5(0) + 12 = 0 - 0 + 12 = 12.
Since the result is not 0, the graph does not contain the point (0, 0), making this statement false.