Draw a common graph f ( x ) = - x2 + 2x + 3 , Mathematics

Assignment Help:

Graph        f ( x ) = - x2 + 2x + 3 .

Solution

It is a parabola in the general form.

                             f ( x ) = ax2 + bx + c

In this form, the x-coordinate of the vertex (on the parabola the highest or lowest point) is

x = -  b/2a and we get the y-coordinate is y = f ( -  b/2a)  .  Hence, for our parabola the coordinates of the vertex will be.

x= - 2/(2(-1)=1

y=f(1) = -(1) 2 + 2(1) +3=4

Hence, the vertex for this parabola is (1,4).

We can also find out which direction the parabola opens from the sign of a.  If a is +ve the parabola opens up & if a is -ve the parabola opens down.  In our case the parabola opens down.

Now, since the vertex is above the x-axis & the parabola opens down we know that we'll have x-intercepts (that means values of x for which we'll have f ( x ) = 0 ) on this graph.  Hence, we'll solve  out the following.

- x2 + 2 x + 3 = 0

x2 - 2 x - 3 = 0

( x - 3) ( x + 1) = 0

Hence, we will have x-intercepts at x = -1 and x = 3 . Notice as well that to make our life simple in the solution process we multiplied everything by -1 to get the coefficient of the x2  positive.  It made the factoring easier.

Following is a sketch of this parabola.

361_common graph 3.png


Related Discussions:- Draw a common graph f ( x ) = - x2 + 2x + 3

Rational, how can you identify if a certain number is rational or irrationa...

how can you identify if a certain number is rational or irrational?

Determine the range of given algorithm, The division algorithm says that wh...

The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(

Quantitative Techniques, You are given that the total frequency is 900 and ...

You are given that the total frequency is 900 and the median 100.48. From the following frequency distribution, find the class frequencies that are missing. Intelligence No. of Int

Determine the average number and probability, 1) At a midway game at the st...

1) At a midway game at the state fair, the probability of winning an individual game is advertised to be 30% ( p = . 3). Suppose 50 people played the game (assume all 50 outcomes

Quartic polynomial, Question: Let f be a quartic polynomial (ie. a poly...

Question: Let f be a quartic polynomial (ie. a polynomial of degree 4). Suppose that f has zeros at -2; 1; 3; 4 and that f(0) = 4. Sketch a graph of f. If f(x) is

Linear programming , Use the simplex method to solve the following LP Probl...

Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0

Linear relations, determine the equation that represent the following lines...

determine the equation that represent the following lines be sure to define your variable and show all of your work

MATLAB, Program of "surface of revolution" in MATLAB

Program of "surface of revolution" in MATLAB

Hi, can i get job of teaching maths here

can i get job of teaching maths here

Introduction to mathematics, We know that one has to deal with ...

We know that one has to deal with numbers in day-to-day life irrespective of his inclination and field of work. Also one cannot refute the fact

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd