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- Algebra and trigonometry
- Polynomial and rational functions
- Quadratic functions
Key equations
general form of a quadratic function |
|
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
(Pcos∅+qsin∅)/(pcos∅-psin∅)
how to answer the activity
how to solve the activity
Chabelita
solve for X,,4^X-6(2^)-16=0
sobhan Singh jina uniwarcity tignomatry ka long answers tile questions
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
If
, ,
are the roots of the equation
3 2 0,
x px qx r
Find the value of
1
.
Parts of a pole were painted red, blue and yellow. 3/5 of the pole was red and 7/8 was painted blue. What part was painted yellow?
Parts of the pole was painted red, blue and yellow. 3 /5 of the pole was red and 7 /8 was painted blue. What part was painted yellow?
Patrick
how I can simplify algebraic expressions
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
lairenea's age is 23yrs
ACKA
Laurene is 46 yrs and Mae is 23 is
Solomon
age does not matter
christopher
solve for X, 4^x-6(2*)-16=0
Alieu
prove`x^3-3x-2cosA=0
(-π<A<=π
create a lesson plan about this lesson
Excusme but what are you wrot?
Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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