Intro to Quadratic Functions (Parabolas) 1

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Question 1 of 5

1. Question
Which of the following shows the graph of $y = 3 x^{2}$ $y=3x^2$ ?
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If $a > 0$ $a>0$ , the parabola is concave up.
If $a < 0$ $a<0$ , the parabola is concave down.
A big $a$ $a$ means a narrow parabola while a small $a$ $a$ means it is wide.

First, check the coefficient of the equation $y =$ $y=$ $3$ $3$ $x^{2}$ $x^2$ .

The value of $a$ $a$ is large, so we can deduce that the graph is narrow.

Next, check the sign of $a$ $a$ .

Because $a = 3$ $a=3$ is positive, we can say that the graph is concave up.

Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
Question 2 of 5

2. Question
Which of the following shows the graph of $y = - x^{2}$ $y=-x^2$ ?
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If $a > 0$ $a>0$ , the parabola is concave up.
If $a < 0$ $a<0$ , the parabola is concave down.
A big $a$ $a$ means a narrow parabola while a small $a$ $a$ means it is wide.

First, check the coefficient of the equation $y =$ $y=$ $-$ $-$ $x^{2}$ $x^2$ .

The value of $a$ $a$ is $- 1$ $-1$ , so we can deduce that the graph is of normal size.

Next, check the sign of $a$ $a$ .

Because $a = - 1$ $a=-1$ is negative, we can say that the graph is concave down.

Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
Question 3 of 5

3. Question
Which of the following shows the graph of $y = \frac{1}{2} x^{2}$ $y=1/2x^2$ ?
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If $a > 0$ $a>0$ , the parabola is concave up.
If $a < 0$ $a<0$ , the parabola is concave down.
A big $a$ $a$ means a narrow parabola while a small $a$ $a$ means it is wide.

First, check the coefficient of the equation $y =$ $y=$ $\frac{1}{2}$ $1/2$ $x^{2}$ $x^2$ .

The value of $a$ $a$ is small, so we can deduce that the graph is wide.

Next, check the sign of $a$ $a$ .

Because $a = \frac{1}{2}$ $a=1/2$ is positive, we can say that the graph is concave up.

Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
Question 4 of 5

4. Question
Which of the following shows the graph of $y = - 4 x^{2}$ $y=-4x^2$ ?
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If $a > 0$ $a>0$ , the parabola is concave up.
If $a < 0$ $a<0$ , the parabola is concave down.
A big $a$ $a$ means a narrow parabola while a small $a$ $a$ means it is wide.

First, check the coefficient of the equation $y =$ $y=$ $- 4$ $-4$ $x^{2}$ $x^2$ .

The value of $a$ $a$ is a large negative number, so we can deduce that the graph is narrow.

Next, check the sign of $a$ $a$ .

Because $a = - 4$ $a=-4$ is negative, we can say that the graph is concave down.

Hence, we can choose from the options which best matches the characteristics of the parabola identified above.
Question 5 of 5

5. Question
Which of the following shows the graph of $y = - \frac{1}{4} x^{2}$ $y=-1/4x^2$ ?
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If $a > 0$ $a>0$ , the parabola is concave up.
If $a < 0$ $a<0$ , the parabola is concave down.
A big $a$ $a$ means a narrow parabola while a small $a$ $a$ means it is wide.

First, check the coefficient of the equation $y =$ $y=$ $- \frac{1}{4}$ $-1/4$ $x^{2}$ $x^2$ .

The value of $a$ $a$ is a small negative number, so we can deduce that the graph is wide.

Next, check the sign of $a$ $a$ .

Because $a = - \frac{1}{4}$ $a=-1/4$ is negative, we can say that the graph is concave down.

Hence, we can choose from the options which best matches the characteristics of the parabola identified above.

Intro to Quadratic Functions (Parabolas) 1

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Quiz summary

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1. Question

Hint

Great Work!

2. Question

Hint

Correct!

3. Question

Hint

Keep Going!

4. Question

Hint

Fantastic!

5. Question

Hint

Excellent!

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