



Key equations
general form of a quadratic function 
$$f(x)=a{x}^{2}+bx+c$$ 
standard form of a quadratic function 
$$f(x)=a{(xh)}^{2}+k$$ 
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 Ushaped curve that can open either up or down.
 The axis of symmetry is the vertical line passing through the vertex. The zeros, or
$\text{\hspace{0.17em}}x\text{}$ intercepts, are the points at which the parabola crosses the
$\text{\hspace{0.17em}}x\text{}$ axis. The
$\text{\hspace{0.17em}}y\text{}$ intercept is the point at which the parabola crosses the
$\text{\hspace{0.17em}}y\text{}$ 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
$\text{\hspace{0.17em}}y\text{}$ 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 realworld problems, including problems involving area and revenue. See
[link] and
[link] .
 The vertex and the intercepts can be identified and interpreted to solve realworld problems. See
[link] .
Section exercises
Verbal
Explain why the condition of
$\text{\hspace{0.17em}}a\ne 0\text{\hspace{0.17em}}$ is imposed in the definition of the quadratic function.
If
$\text{\hspace{0.17em}}a=0\text{\hspace{0.17em}}$ then the function becomes a linear function.
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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.
$f\left(x\right)=2{x}^{2}10x+4$
Minimum is
$\text{\hspace{0.17em}}\frac{17}{2}\text{\hspace{0.17em}}$ and occurs at
$\text{\hspace{0.17em}}\frac{5}{2}.\text{\hspace{0.17em}}$ Axis of symmetry is
$\text{\hspace{0.17em}}x=\frac{5}{2}.$
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Minimum is
$\text{\hspace{0.17em}}\frac{17}{16}\text{\hspace{0.17em}}$ and occurs at
$\text{\hspace{0.17em}}\frac{1}{8}.\text{\hspace{0.17em}}$ Axis of symmetry is
$\text{\hspace{0.17em}}x=\frac{1}{8}.$
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$f(x)=\frac{1}{2}{x}^{2}+3x+1$
Minimum is
$\text{\hspace{0.17em}}\frac{7}{2}\text{\hspace{0.17em}}$ and occurs at
$\text{\hspace{0.17em}}\mathrm{3.}\text{\hspace{0.17em}}$ Axis of symmetry is
$\text{\hspace{0.17em}}x=\mathrm{3.}$
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For the following exercises, determine the domain and range of the quadratic function.
Questions & Answers
nothing up todat yet
Miranda
aap konsi country se ho
jai
which language is that
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
state and prove Cayley hamilton therom
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.
Miranda
algebra is a branch of the mathematics to calculate expressions follow.
Miranda
Miranda Drice would you mind teaching me mathematics? I think you are really good at math.
I'm not good at it. In fact I hate it. 😅😅😅
Jeffrey
lolll who told you I'm good at it
Miranda
something seems to wispher me to my ear that u are good at it. lol
Jeffrey
lolllll if you say so
Miranda
but seriously, Im really bad at math. And I hate it. But you see, I downloaded this app two months ago hoping to master it.
Jeffrey
which grade are you in though
Miranda
oh woww I understand
Miranda
haha. already finished college
Jeffrey
how about you? what grade are you now?
Jeffrey
I'm going to 11grade
Miranda
how come you finished in college and you don't like math though
Miranda
gotta practice, holmie
Steve
if you never use it you won't be able to appreciate it
Steve
I don't know why. But Im trying to like it.
Jeffrey
yes steve. you're right
Jeffrey
what is the solution of the given equation?
please where is the equation
Miranda
answer and questions in exercise 11.2 sums
how do u calculate inequality of irrational number?
Alaba
and I will walk you through it
Chris
cos (z)= cos z .
Swadesh
what is the identity of 1cos²5x equal to?
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
what is the function of sine with respect of cosine , graphically
sinx sin2x is linearly dependent
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls
How look for the general solution of a trig function
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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