Lesson 8 Quadratic Quarters Practice Understanding

Ready

Use the Pythagorean theorem to find the missing side of each right triangle $(a^{2} + b^{2} = c^{2})$ . Write your answer using the $\sqrt{}$ and as a decimal. (Round to hundredths place.)

1.

2.

3.

4.

5.

6.

Set

One piece of information is given. Use it to fill in the missing information.

7.

Function in standard form: $f (x) = x^{2} + 5 x - 6$

Function in factored form:

$x$ -intercepts:

$y$ -intercept:

Graph of the function:

8.

Function in standard form: $f (x) = x^{2} - 9$

Function in factored form:

$x$ -intercepts:

$y$ -intercept:

Vertex:

Line of symmetry:

Domain:

Range:

9.

Function in standard form: $h (x) = - x^{2} + 4 x$

Vertex:

Maximum or minimum:

Interval of increase:

Interval of decrease:

Solutions to the equation: $- x^{2} + 4 x = 0$

Line of symmetry:

Domain:

Range:

10.

The side of a square is $(x + 3) inches$ and the area is $8 {in}^{2}$ .

Solution using graphical method:

Solution using algebraic method:

Solutions written with simplified square roots:

Solutions written as decimals:

Go

In each problem, the $x$ -intercepts of a parabola are given. Write the equation of the parabola in factored form and in standard form, given that the coefficient of $x^{2}$ is $1$ . (There is no stretch factor.)

11.

$(5, 0)$ and $(8, 0)$

12.

$(- 4, 0)$ and $(3, 0)$

13.

$(6, 0)$ and $(- 6, 0)$

14.

$(- 9, 0)$ and $(- 1, 0)$

15.

$(7, 0)$ and $(0, 0)$

16.

This parabola has one $x$ -intercept at $3$ .