Lesson 10 I’ve Got a Fill-in Practice Understanding

Ready

A golf pro practices his swing by driving golf balls off the edge of a cliff into a lake. The height of the ball above the lake (measured in meters) as a function of time (measured in seconds and represented by the variable $t$ ) from the instant of impact with the golf club is the following:

$h (t) = 58.8 + 19.6 t - 4.9 t^{2}$

The expressions shown are equivalent:

$- 4.9 t^{2} + 19.6 t + 58.8$ standard form

$- 4.9 (t - 6) (t + 2)$ factored form

$- 4.9 {(t - 2)}^{2} + 78.4$ vertex form

1.

Which expression is the most useful for finding how many seconds it takes for the ball to hit the water? Why?

2.

Which expression is the most useful for finding how many seconds it takes for the ball to reach its maximum height? Why?

3.

Which expression is the most useful for finding the maximum height of the ball? Justify your answer.

4.

If you wanted to know the height of the ball at exactly $3.5$ seconds, which expression would help the most to find the answer? Why?

5.

If you wanted to know the height of the cliff above the lake, which expression would you use? Why?

Set

One representation of a quadratic function is given. Fill in the missing representations and provide the indicated information.

6.

Factored form: $y = (x + 5) (x - 3)$

a.

Standard form

b.

Vertex form

c.

Which features of this function are most easily identified from the given equation? State them.

d.

Graph

7.

Vertex form: $y = - 3 {(x - 1)}^{2} + 3$

a.

Standard form

b.

Factored form

c.

Which features of this function are most easily identified from the given equation? State them.

d.

Graph

8.

Standard form: $y = - x^{2} + 10 x - 25$

a.

Vertex form

b.

Factored form

c.

Which features of this function are most easily identified from the given equation? State them.

d.

Graph

9.

a.

Standard form

b.

Vertex form

c.

Factored form

d.

Which features of this function are most easily identified from the given graph? State them.

10.

a.

Show the first differences and the second differences on the given table.

b.

Standard form

c.

Vertex form

d.

Graph

Go

Multiply each pair of binomials using the Distributive Property.

11.

$(x + 16) (x - 4)$

12.

$(x + 8) (x - 8)$

13.

$(x + 16) (x + 4)$

14.

$(x - 8) (x - 8)$

Factor the following quadratic expressions, if possible. Some will not factor; if they don’t factor, state that it does not factor.

15.

$x^{2} - 5 x + 6$

16.

$x^{2} - 7 x + 6$

17.

$x^{2} - 5 x - 36$

18.

$m^{2} + 16 m + 63$

19.

$s^{2} - 3 s - 1$

20.

$x^{2} + 7 x + 2$

21.

$x^{2} + 14 x + 49$

22.

$x^{2} - 9$

23.

$c^{2} + 11 c + 3$

24.

Which quadratic expression above could represent the area of a square? Explain.

25.

Would any of the expressions above NOT be the side lengths for a rectangle? Explain.