Quadratic functions

Introductory and Intermediate Algebra for College Students

Write the equation of each parabola in $f(x)=a(x-h)^{2}+k$ form.
Vertex: (-3,-4)$;$ The graph passes through the point (1,4)

Quadratic Equations and Functions

Quadratic Functions and Their Graphs

01:45

Introductory and Intermediate Algebra for College Students

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
The graph of $f(x)=-2(x+4)^{2}-8$ has one $y$ -intercept and two $x$ -intercepts.

Quadratic Equations and Functions

Quadratic Functions and Their Graphs

01:21

Introductory and Intermediate Algebra for College Students

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
No quadratic functions have a range of $(-\infty, \infty)$

Quadratic Equations and Functions

Quadratic Functions and Their Graphs

Using Quadratic Functions as Models

145 Practice Problems

05:07

Algebra and Trigonometry

A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest?

Polynomial and Rational Functions

Quadratic Functions

03:09

Algebra and Trigonometry

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry.
$$h(t)=-4 t^{2}+6 t-1$$

Polynomial and Rational Functions

Quadratic Functions

01:23

Calculus and Its Applications

The quantity sold $x$ of a plasma television is inversely proportional to the price $p$. If 85,000 plasma TVs sold for $\$ 2900$ each, how many will be sold if the price is $\$ 850$ each?

Functions, Graphs, and Models

Nonlinear Functions and Models

Using Quadratic Models to Represent Data

56 Practice Problems

04:48

Elementary Statistics

Listed below are mean amounts of carbon dioxide concentrations (parts per million) in our atmosphere for each decade, beginning with the 1880 s. Find the best model and then predict the value for $2090-2099 .$ Comment on the result.
$$\begin{array}{rrrrrrrr}292 & 294 & 297 & 300 & 304 & 307 & 309 & 314 & 320 & 331 & 345 & 360 & 377\end{array}$$

Correlation and Regression

Nonlinear Regression

02:21

Elementary Statistics

According to Benford's law, a variety of different data sets include numbers with leading (first) digits that occur with the proportions listed in the following table.
$$\begin{array}{l|c|c|c|c|c|c|c|c|c}\hline \text { Leading Digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Proportion } & 0.301 & 0.176 & 0.125 & 0.097 & 0.079 & 0.067 & 0.058 & 0.051 & 0.046 \\\hline\end{array}$$

Correlation and Regression

Nonlinear Regression

01:31

Elementary Statistics

The table lists intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity.
$$\begin{array}{l|l|l|l|l|l}\hline \text { Sound Intensity } & 316 & 500 & 750 & 2000 & 5000 \\\hline \text { Scale Value } & 25.0 & 27.0 & 28.75 & 33.0 & 37.0 \\\hline\end{array}$$

Correlation and Regression

Nonlinear Regression

Quadratic Inequalities

109 Practice Problems

01:49

Precalculus : Building Concepts and Connections

Solve the quadratic inequality.
$$x^{2} \leq 4$$

Polynomial and Rational Functions

Polynomial and Rational Inequalities

02:53

Precalculus : Building Concepts and Connections

Solve the inequality algebraically or graphically.
$$x^{2}-x+1 \geq 0$$

More About Functions and Equations

Quadratic Inequalities

02:30

Precalculus : Building Concepts and Connections

Solve the inequality algebraically or graphically.
$$2 x^{2}-3 x<1$$

More About Functions and Equations

Quadratic Inequalities

The Square Root Property and Completing the Square

34 Practice Problems

02:28

Prealgebra and Introductory Algebra

For a quadratic equation of the form $x^{2}+b x+c=0,$ the sum of the solutions is equal to the opposite of $b$, and the product of the solutions is equal to $c .$ For example, the solutions of the equation $x^{2}+5 x+6=0$ are $-2$ and $-3 .$ The sum of the solutions is
$-5,$ the opposite of the coefficient of $x$. The product of the solutions is $6,$ the constant term. This is one way to check the solutions of a quadratic equation. Use this method to determine whether the given numbers are solutions of the equation. If they are not solutions of the equation, find the solutions.
$$x^{2}-8 x-14=0 ;-4+\sqrt{15} \text { and }-4-\sqrt{15}$$

Quadratic Equations

Solving Quadratic Equations by Using the Quadratic Formula

00:43

Prealgebra and Introductory Algebra

Explain why the equation $(x-2)^{2}=-4$ does not have a real number solution.

Quadratic Equations

Solving Quadratic Equations by Completing the Square

02:02

Prealgebra and Introductory Algebra

For Exercises 56 to $58,$ solve.
$$\sqrt{2 x+7}-4=x$$

Quadratic Equations

Solving Quadratic Equations by Completing the Square

The Quadratic Formula

16 Practice Problems

01:24

Prealgebra and Introductory Algebra

Factoring, completing the square, and using the quadratic formula are three methods of solving quadratic equations. Describe each method, and cite the advantages and disadvantages of each.

Quadratic Equations

Solving Quadratic Equations by Using the Quadratic Formula

01:56

Prealgebra and Introductory Algebra

Solve by using the quadratic formula. Approximate the solutions to the nearest thousandth.
$$5 v^{2}-v-5=0$$

Quadratic Equations

Solving Quadratic Equations by Using the Quadratic Formula

00:33

Prealgebra and Introductory Algebra

True or false? If you use the quadratic formula to solve $a x^{2}+b x+c=0$ and get rational solutions, then you could have solved the equation by factoring.

Quadratic Equations

Solving Quadratic Equations by Using the Quadratic Formula

Quadratic Functions and Their Graphs

8 Practice Problems

01:14

Prealgebra and Introductory Algebra

Determine the $x$ - and $y$ -intercepts.
$$y=x^{2}+5 x-6$$

Quadratic Equations

Graphing Quadratic Equations in Two Variables

01:28

Prealgebra and Introductory Algebra

Graph.
(GRAPH CANNOT COPY)
$$y=x^{2}-4 x$$

Quadratic Equations

Graphing Quadratic Equations in Two Variables

00:46

Prealgebra and Introductory Algebra

Evaluate the function for the given value of $x$.
$$f(x)=-2 x^{2}+2 x-1 ; x=-3$$

Quadratic Equations

Graphing Quadratic Equations in Two Variables

Quadratic and Other Nonlinear Inequalities

5 Practice Problems

03:30

Beginning and Intermediate Algebra

Solve each quadratic inequality. Graph the solution set and write the solution in interval notation.
$$c^{2}+5 c<36$$

Conic Sections, Nonlinear Inequalities, and Nonlinear Systems

Quadratic and Rational Inequalities

00:27

Intermediate Algebra

A. Solve: $x^{2}-x-12>0$
B. Find a rational inequality in one variable that has the same solution set as the quadratic inequality in part (a).

Quadratic Equations, Functions, and Inequalities

Quadratic and Other Nonlinear Inequalities

01:47

Intermediate Algebra

The number of people $n$ in a mall is modeled by the formula
$$
n=-100 x^{2}+1,200 x
$$
where $x$ is the number of hours since the mall opened. If the mall opened at 9 A.M., when were there $2,000$ or more people in it?

Quadratic Equations, Functions, and Inequalities

Quadratic and Other Nonlinear Inequalities