A student is analyzing the transformations applied to the parent function $$f(x) = x^2$$ to produce $$g(x) = -3(x + 2)^2 + 7$$ . The student claims that the graph of $$g(x)$$ opens downward, is narrower than the parent function, shifts 2 units to the left, and shifts 7 units up. Which of the following best evaluates the student's claim and explains the reasoning?

The student is correct; $$a = -3$$ causes the graph to open downward and stretch vertically, $$c = -2$$ shifts the graph 2 units to the left, and $$d = 7$$ shifts the graph 7 units up

The student is incorrect; $$a = -3$$ causes the graph to open downward but makes it wider, $$c = -2$$ shifts the graph 2 units to the right, and $$d = 7$$ shifts the graph 7 units up

The student is incorrect; $$a = -3$$ causes the graph to open upward and stretch vertically, $$c = -2$$ shifts the graph 2 units to the left, and $$d = 7$$ shifts the graph 7 units down

The student is incorrect; $$a = -3$$ causes the graph to open downward and stretch vertically, $$c = -2$$ shifts the graph 2 units to the right, and $$d = 7$$ shifts the graph 7 units up

Given the quadratic function $$f(x) = x^2 + 4x + 1$$ , what are the zeros of the function?

$$x = -2 + \sqrt{3}$$ and $$x = -2 - \sqrt{3}$$

Exploring Quadratic Functions Quiz

Authored by Laura Sutherland

Mathematics

9th Grade

TEKS covered

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the vertex form of a quadratic function?

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TEKS.A.6.B

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

All real numbers

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TEKS.A.6.A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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TEKS.A.7.A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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TEKS.A.6.B

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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TEKS.A.8.A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

All real numbers

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TEKS.A.6.A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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TEKS.A.7.C

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