Graphing Quadratic Functions Worksheet

**Page 1**

1.

Katie says without drawing the graph of $y$ = - 2$x$^{2} + 4 , we can find out if its vertex is above or below the point (0, 0) . Is she correct?

a. | No | ||

b. | Yes |

It is possible to predict without drawing the graph of

For

[Compare with

Consider

If

If

Here we have

Correct answer : (2)

2.

Identify the list that shows all the possible rational roots of the equation 4$x$^{13} + 4$x$^{7} + 2$x$ + 5 = 0.

a. | ± $\frac{1}{2}$, ± $\frac{1}{4}$, ± $\frac{5}{2}$, ± $\frac{5}{4}$ | ||

b. | ± 1, ± $\frac{1}{2}$, ± $\frac{1}{4}$ , ± 5 | ||

c. | ± 1, ± $\frac{1}{2}$, ± $\frac{1}{4}$, ± 5, ± $\frac{5}{2}$, ± $\frac{5}{4}$ | ||

d. | ± 1, ± 5 |

Factors of 5 are ± 1 and ± 5.

Leading coefficient = 4

Factors of 4 are ± 1, ± 2, and 4.

Rational root =

Correct answer : (3)

3.

At how many points does the graph of $y$ = $x$^{2} - 3$x$ - 40 intersect the $x$-axis?

a. | one | ||

b. | two | ||

c. | three | ||

d. | zero |

For

[Substitute

Therefore, the points at which the graph intersect the

So, the graph intersects the

Correct answer : (2)

4.

At how many points does the graph of $y$ = $x$^{2} - 2$x$ + 1 intersect the $x$-axis?

a. | zero | ||

b. | two | ||

c. | cannot be determined | ||

d. | one |

Correct answer : (4)

5.

At how many points does the graph of $y$ = $x$^{2} + 2$x$ + 3 intersect the $x$-axis?

a. | cannot be determined | ||

b. | two | ||

c. | one | ||

d. | zero |

Correct answer : (4)

6.

At how many points does the graph of $y$ = $x$^{2} - 12$x$ + 36 intersect the $x$-axis?

a. | cannot be determined | ||

b. | zero | ||

c. | two | ||

d. | one |

Correct answer : (4)

7.

At how many points does the graph of $y$ = $x$^{2} - 4$x$ - 5 intersect the $x$-axis?

a. | two | ||

b. | cannot be determined | ||

c. | one | ||

d. | zero |

Correct answer : (1)

8.

At how many points does the graph of $y$ = 2$x$^{2} - 5$x$ - 25 intersect the $x$-axis?

a. | zero | ||

b. | two | ||

c. | cannot be determined | ||

d. | one |

Correct answer : (2)

9.

At how many points does the graph of $y$ = $x$^{2} - 3$x$ - 4 intersect the $x$-axis?

a. | zero | ||

b. | one | ||

c. | two | ||

d. | cannot be determined |

Correct answer : (3)

10.

What is the effect of the constant factor on the slope of the functions $y$_{1} = 5$x$^{2} - 2$x$ + 11 and $y$_{2} = $x$^{2} - $\frac{2}{5x}$ + $\frac{11}{5}$?

a. | cannot be determined | ||

b. | no change | ||

c. | more steeper | ||

d. | less steeper |

Correct answer : (4)