SOLUTION: Complete each of the following for the function g(x)=-3x^2-6x+1 a.Find the vertex of g(x) b.Find the x-intercept c.Find the y-intercept

Question 224743: Complete each of the following for the function g(x)=-3x^2-6x+1
a.Find the vertex of g(x)
b.Find the x-intercept
c.Find the y-intercept
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Complete each of the following for the function g(x)=-3x^2-6x+1

a.Find the vertex of g(x)

b.Find the x-intercept

c.Find the y-intercept

Step 1. The general formula for a parabola is where x=a and y=b is the vertex or at point (a,b). Here, c is a constant.

Step 2. Put in standard form by completing the square in x with the following steps.

where we added zero 0=-3+3 to complete the square

Factor out -3 in the first three terms

Subtract 4 from both sides of the equation

ANSWER: So the vertex is located at point (-1, 4)

Step 3. To find the x-intercept, set g(x)=y=0. We use the quadratic formula given as

where a=-3, b=-6 and c=1

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=48 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -2.15470053837925, 0.154700538379251. Here's your graph:

Step 4. To find the y-intercept set x=0 in g(x)=y=-3x^2-6x+1

or y=1.

The y-intercept is at (0,1) which is consistent with the above graph.

I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

RELATED QUESTIONS
Given the function g described by g(x)=6x, find each of the following, (a) g(-4) (b)... (answered by solver91311)

Given that g(x)= 3x^2-5x+4, find each of the following a) g(0) b) g(-1) c) g(3) d)... (answered by jim_thompson5910)

For the given function, (a) determine whether the graph opens upward or downward, (b)... (answered by stanbon)

Given that g(x)=3x^2+2x+3, find each of the following. A) g(-1)... (answered by jim_thompson5910)

For g(x)= -x^2 + 6x - 5 complete the following parts. a) Determine... (answered by josgarithmetic)

Find the Domain of the following: a) g(x) = 5^x b) g(x) = In(x-4) c) g(t) = log(t-2)... (answered by dhartman0220)

Find the x-intercepts, y-intercepts and the vertex of... (answered by lwsshak3)

a) Sketch the graph of g: x|--> {{{x^2+6x+7}}} b) Explain why g for x(belongs to)... (answered by Fombitz)

give the given function g described by g(x) = 5x, find each of the following: (a) g(-10)= (answered by anantha)