SOLUTION: My question is if the vertex of f(x)=-x^2+bx+8 has y-coordinate 17 and is in the second quadrant, find b.

Algebra.Com
Question 103792This question is from textbook Precalculus A GRAPHING APPROACH
: My question is if the vertex of f(x)=-x^2+bx+8 has y-coordinate 17 and is in the second quadrant, find b. This question is from textbook Precalculus A GRAPHING APPROACH

Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation


To find the x-coordinate of the vertex, simply use this formula




So plug in a=-1


Simplify


So the x value of the vertex is


Now plug this value in, as well as f(x)=17, to solve for b


Plug in and f(x)=17



Square to get


Multiply


Multiply both sides by 4 to eliminate any fractions


Subtract 68 from both sides


Combine like terms


Factor the right side


Now set each factor equal to zero and solve


or


or


But since the vertex is in the second quadrant, the answer is




Notice if we plug in b=-6 into , we get


and if we graph the equation we get:




and we can see that the vertex has a y value at y=17 and it lies in the second quadrant. So our answer is verified.

Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
vertex=(h,k)=(h,17)
-(x-h)^2+17=-x^2+bx+8
We need a -9 to add to 17 to give 8. a has to be negative to give -x^2. h must be negative so that the vertex can be in the 2nd quadrant.
h=-3
-(x+3)^2=-(x^2+6x+9)+17
=-x^2-6x-9+17
=-x^2-6x+8
b=-6 Ans.
Ed

RELATED QUESTIONS

Find b such that f(x)=-2x^2+bx-30 has a maximum value of 2 and the vertex is located in... (answered by stanbon)
My problem is if the vertex of f(x)=x^2+bx+c is at (2,4), find b and... (answered by scott8148,edjones)
find the equation of the axis of symmetry and the coordinates of the vertex of the graph... (answered by mathsteacher)
Please help! I am lost in how to figure this out: f(x)= -2x^2+2x+8 This one has... (answered by Edwin McCravy)
I am having difficulty with a question. The problems is as follows: A parabola has an... (answered by RAY100,jsmallt9,Alan3354)
find the vertex, the line of symmetry, the maximum or minimum value of the quatratic... (answered by ewatrrr)
The question is... F(x)=x^2+6x-2 Find h, the x-coordinate of the vertex of this... (answered by jim_thompson5910)
find sin(a+b)if sin(a)=8/17 and a is in the first quadrant and tan(b)= -7/24 and b is in... (answered by norymae)
determine the quadratic function f whose vertex is (2,-4) and passes through (1,-2)... (answered by reviewermath,DrBeeee)