1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elenna [48]
3 years ago
8

F(x)=2x^2-x-10 part a: what are the X intercepts of the graph of f(x)? Show your work

Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0
A. x intercepts are where the graph hits the x axis or where f(x)=0
0=2x^2-x-10
solve
hmm
we can use the ac method
multiply 2 and -10 to get -20
what 2 numbers muliply to get -20 and add to get -1 (the coefint of the x term)
-5 and 4
split the midd into that
0=2x^2+4x-5x-10
group
0=(2x^2+4x)+(-5x-10)
factor
0=2x(x+2)-5(x+2)
undistribute
0=(x+2)(2x-5)
set each to 0
0=x+2
0=-2

0=2x-5
5=2x
5/2=x

x intercepts are at x=-2 and 5/2 or the points (-2,0) and (5/2,0)


B. ok, so for f(x)=ax^2+bx+c
if a>0, then the parabola opens up and the vertex is a minimum
if a<0 then the parabola opens down and the vertex is a max

f(x)=2x^2-x-10
2>0
opoens up
vertex is minimum

ok, the vertex

the x value of  the vertex in f(x)=ax^2+bx+c= is -b/(2a)
the y value of the vertex is f(-b/(2a)) so
given
f(x)=2x^2-x-10
a=2
b=-1
-b/2a=-(-1)/(2*2)=1/4
f(1/4)=2(1/4)^2-(1/4)-10
f(1/4)=2(1/16)-1/4-10
f(1/4)=1/8-1/4-10
f(1/4)=1/8-2/8-80/8
f(1/4)=-81/8
so the vertex is (1/4,-81/8) or (0.25,-10.125)


C. graph the x intercepts and the vertex
the vertex is min and the graph goes through the x intercepts
You might be interested in
Wayne spends 1/6th of an hour walking his dog. How much time does Wayne spend walking his dog in a week? *
Mila [183]

Answer:

10 minutes

Step-by-step explanation:

This is somewhat of a trick question and also incomplete.

Assuming he walks his dog 1/6th of an hour each week, he walks his dog 10 minutes per week.

If this is incorrect please tell me the complete question

3 0
2 years ago
How do I find the Axis of Symmetry for a parabola
soldier1979 [14.2K]

Answer:

Explanation given below.

Step-by-step explanation:

The first step is to put the parabola in the form  ax^2+bx+c , which is the <em>standard form of a parabola</em>

<em />

<u>Note:</u> a is the coefficient before x^2 term, b is the coefficient before x term, and c is the independent constant term

The axis of symmetry divides the parabola symmetrically. The axis of symmetry has the equation  x=-\frac{b}{2a}

Where <em><u>a and b are the respective values shown above</u></em>

<em><u /></em>

So, that is how you get the axis of symmetry of any parabola.

4 0
3 years ago
Read 2 more answers
PLEASE HELP FAST!! Use a graphing calculator to graph the function y=90tan2x on the interval 0 degrees&lt; x &lt; 180 degrees an
Ann [662]

Answer: use desmos graphing calculator

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Every 124 minutes ½ of a drug dosage remains in the body
Vitek1552 [10]

Answer: Is this a fun fact??? If it is then this is not related to math at all

Step-by-step explanation:

4 0
2 years ago
Which of the box plots A,B Or C show a sample that has
Paul [167]
The answer is C
This is a box plot diagram also know as a box and whisker plot as you probably see where it gets its name from, to find which diagram is correct you need to look for the following things. First we need to see if the median which in this case is 12 is in on the correct place which in C it is nicely lines up to 12 in the center of the diagram. The median for a the line in the line in the middle of the box plot.
Now we need to have a look at our lower quartile and see that it does start at 6 and the upper quartile does end at 16 these are the lines that make the rectangle shape in the centre lucky for us in C they do. Then we need to see if the lines that run horizontally through the box ( may also be called the whiskers) start at the minimum 3 and end at the maximum of 22 which they do so in the end gives C is true only diagram with all of these in.
Hope this helps !
8 0
3 years ago
Other questions:
  • I need help bad this is so hard i don't know what to do
    9·1 answer
  • Name two triangles that are congruent by the ASA Postulate.
    6·1 answer
  • Solve the system using the method of you choice: <br> -x + 4y = 12 <br><br> 5x - 2y = -6
    9·1 answer
  • What is the reciprocal of 9/11
    8·2 answers
  • A TV has a height:width in a ratio 9:16 In a scale drawing the height is 4.5 cm. What would the width be?
    13·2 answers
  • Find the 67th term of the arithmetic sequence –17, -23, -29,...
    8·2 answers
  • Which graph represents all of the solutions of 3n–15≤ -3?
    15·2 answers
  • Sorry guys i really hate geometry
    7·1 answer
  • Please help me with this.<br> (t+2) + (t-3)=9<br> Transform to standard equation form ax^2+bx+c=0
    7·1 answer
  • Francesca is growing 1/2 inch each year. How many years will it take her to grow 6 inches?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!