```Question 502349
Describe the graph of the quadratic function f(x) = -x2 + 7x + 8 by identifying the following:
the concavity of the graph;
the vertex;
the line of symmetry;
the x-intercepts and y intercept;
Describe the graph algebraically; in other words, without graphing.
**
f(x)=-x2+7x+8
completing the square
y=-(x^2-7x+49/4)+8+49/4
y=-(x-7/2)^2+32/4+49/4
y=-(x-7/2)^2+81/4
This is an equation of a parabola of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. A is a multiplier which affects the steepness of the curve.
For given equation:
Vertex: (7/2,81/4)
The negative sign of the lead coefficient means that the parabola opens downward.
The line of symmetry or axis of symmetry: x=7/2
..
y-intercept: set x=0, then solve for y
y-intercept=8
..
x-intercept: set y=0, then solve for x
-x2+7x+8=0
x^2-7x-8=0
(x-8)(x+1)=0
x-intercepts: 8 and -1
..
General description of graph:
This is a parabola which opens downwards, with a maximum of 81/4, at x=7/2.
Curve cuts thru the y-axis at 8, and thru the x-axis at 8 and -1
Curve is symmetrical about the line x=7/2```