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Home
- College algebra
- Polynomial and rational functions
- Quadratic functions
Key equations
general form of a quadratic function |
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standard form of a quadratic function |
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Key concepts
- A polynomial function of degree two is called a quadratic function.
- The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that can open either up or down.
- The axis of symmetry is the vertical line passing through the vertex. The zeros, or
intercepts, are the points at which the parabola crosses the
axis. The
intercept is the point at which the parabola crosses the
axis. See
[link] ,
[link] , and
[link] .
- Quadratic functions are often written in general form. Standard or vertex form is useful to easily identify the vertex of a parabola. Either form can be written from a graph. See
[link] .
- The vertex can be found from an equation representing a quadratic function. See
[link]
.
- The domain of a quadratic function is all real numbers. The range varies with the function. See
[link] .
- A quadratic function’s minimum or maximum value is given by the
value of the vertex.
- The minimum or maximum value of a quadratic function can be used to determine the range of the function and to solve many kinds of real-world problems, including problems involving area and revenue. See
[link] and
[link] .
- The vertex and the intercepts can be identified and interpreted to solve real-world problems. See
[link] .
Section exercises
Verbal
What two algebraic methods can be used to find the horizontal intercepts of a quadratic function?
If possible, we can use factoring. Otherwise, we can use the quadratic formula.
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Algebraic
For the following exercises, rewrite the quadratic functions in standard form and give the vertex.
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.
For the following exercises, determine the domain and range of the quadratic function.
Questions & Answers
calculate molarity of NaOH solution when 25.0ml of NaOH titrated with 27.2ml of 0.2m H2SO4
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Kaddija
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what is the best way to define periodic table for jamb
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what is isolation of organic compounds
Read Chapter 6, section 5
Dr
Read Chapter 6, section 5
Kareem
Atomic radius is the radius of the atom and is also called the orbital radius
Kareem
atomic radius is the distance between the nucleus of an atom and its valence shell
Amos
Read Chapter 6, section 5
paulino
Bohr's model of the theory atom
when a gas is compressed why it becomes hot?
ATOMIC
It has no oxygen then
Goldyei
read the chapter on thermochemistry...the sections on "PV" work and the First Law of Thermodynamics should help..
Dr
Which element react with water
an increase in the pressure of a gas results in the decrease of its
definition of the periodic table
what were atoms composed of?
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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