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Consider the quadratic function f(x)=x²-5x + 12. Which statements are true about the function and i

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).

User Newbee
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1 Answer

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23 votes

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 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.

User Diggingforfire
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