SOLUTION: response to the following: Describe the graph of the quadratic function f(x) = x^2 - 7x - 8 by identifying the following: the concavity of the graph; the vertex; the line

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: response to the following: Describe the graph of the quadratic function f(x) = x^2 - 7x - 8 by identifying the following: the concavity of the graph; the vertex; the line      Log On


   

Question 395691: response to the following:

Describe the graph of the quadratic function f(x) = x^2 - 7x - 8 by identifying the following:
the concavity of the graph;
the vertex;
the line of symmetry;
the x-intercepts and y intercept;

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

f(x) = x^2 - 7x - 8

finding x-intercepts when f(x) = 0

x^2 - 7x - 8 = 0

factoring

(x-8)(x+1)=0 Note:SUM of the inner product(-8x) and the outer product(x) = -7x

(x-8)= 0 x = 8    | x-intercept Pt(8,0)

(x+1)=0  x = -1   | x-intercept Pt(-1,0)

finding y-intercepts when x = 0

f(0) = x^2 - 7x - 8  = -8  |y-intercept Pt(0,-8)

finding the vertex by completing the square:

the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

f(x) = x^2 - 7x - 8

f(x) = 1*(x - 7/2)^2 - 49/4 - 8

f(x) = (x - 7/2)^2 - 81/4  Vertex is Pt(7/2,-81/4) Line of symmetry x = 7/2

 a = 1 > 0  Parabola opens upward