Table of contents

1. Review of Real Numbers2h 43m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

3. Solving Word Problems2h 46m

Introduction to Problem Solving
37m

Formulas
25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
15m

Composition of Functions
17m

5. Systems of Linear Equations1h 53m

Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

6. Exponents, Polynomials, and Polynomial Functions3h 17m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
38m

Special Products
34m

7. Factoring2h 49m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
41m

Quadratic Equations & Applications
41m

8. Rational Expressions and Functions3h 44m

Simplifying Rational Expressions
42m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

9. Roots, Radicals, and Complex Numbers2h 33m

Introduction to Radical Expressions
11m

Simplifying Radical Expressions
27m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

10. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

11. Inverse, Exponential, & Logarithmic Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

Introduction to Logarithmic Functions
26m

12. Conic Sections & Systems of Nonlinear Equations58m

Graphing Circles
32m

Ellipses
15m

Parabolas
10m

13. Sequences, Series, and the Binomial Theorem1h 51m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
29m

Factorials
13m

10. Quadratic Equations and Functions

Graphing Quadratic Equations

Intermediate Algebra

10. Quadratic Equations and Functions

Graphing Quadratic Equations

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Multiple Choice

State the vertex, intercepts, and domain & range for each quadratic.
$y = - 2 x^{2} + 11$

Vertex: $$\left$(0,$\right$.$\sqrt{\frac{11}{2}$})$ ; $x$ -intercepts: $$\left$($\sqrt{\frac{11}{2}$,0}$\right$),$\left$(-$\sqrt{\frac{11}{2}$,0}$\right$)$ ; $y$ -intercept: $$\left$(0,11$\right$)$ ; Domain: $$\left$(-$\infty$,$\infty\]\right$)$ ; Range: $$\left\]\lbrack$11,$\right$.$\infty$)$

Vertex: $$\left$(0,11$\right$)$ ; $x$ -intercepts: $$\left$($\sqrt{\frac{11}{2}$,0}$\right$),$\left$(-$\sqrt{\frac{11}{2}$,0}$\right$)$ ; $y$ -intercept: $$\left$(0,0$\right$)$ ; Domain: $$\left$(-$\infty$,$\infty\]\right$)$ ; Range: $$\left\]\lbrack$11,$\right$.$\infty$)$

Vertex: $$\left$(0,11$\right$)$ ; $x$ -intercepts: $$\left$($\sqrt{\frac{11}{2}$,0}$\right$),$\left$(-$\sqrt{\frac{11}{2}$,0}$\right$)$ ; $y$ -intercept: $$\left$(0,11$\right$)$ ; Domain: $$\left$(-$\infty$,$\infty\]\right$)$ ; Range: $\left\)(-$\infty$,11\(\right\]\rbrack$

Vertex: $$\left$(11,0$\right$)$ ; $x$ -intercepts: $$\left$($\sqrt{\frac{11}{2}$,0}$\right$),$\left$(-$\sqrt{\frac{11}{2}$,0}$\right$)$ ; $y$ -intercept: $$\left$(0,0$\right$)$ ; Domain: $$\left$(-$\infty$,$\infty\]\right$)$ ; Range: $\left\)(-$\infty$,11\(\right\]\rbrack$

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Verified step by step guidance

Identify the quadratic function given: $y = -2x^2 + 11$.

Find the vertex using the formula for the vertex of a parabola $y = ax^2 + bx + c$, which is at $x = -\frac{b}{2a}$. Here, $a = -2$ and $b = 0$, so the vertex's $x$-coordinate is \$0$. Substitute $x=0$ into the function to find the $y$-coordinate of the vertex.

Determine the $x$-intercepts by setting $y=0$ and solving the equation $-2x^2 + 11 = 0$. Rearrange to isolate $x^2$, then take the square root of both sides to find the two $x$-intercepts.

Find the $y$-intercept by evaluating the function at $x=0$, which gives the point where the graph crosses the $y$-axis.

State the domain and range: The domain of any quadratic function is all real numbers, $(-\infty, \infty)$. Since the parabola opens downward (because $a < 0$), the range is all $y$-values less than or equal to the vertex's $y$-coordinate.

6:28m

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Struggling with Intermediate Algebra?

State the vertex, intercepts, and domain & range for each quadratic.y=−2x2+11y=-2x^2+11

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State the vertex, intercepts, and domain & range for each quadratic.
$y = - 2 x^{2} + 11$