f(x)=-x^2+8x+1

Question

find the vertex the line of symmetry, the maximum or minimum vale of the quadratic function, and graph the function.

Answer 1

f (x ) = -x ² + 8x + 1

The above quadratic equation represents standard form of parabola y  = ax ^2 + bx + c .

a  = -1 , b  = 8 , c  = 1.

Line of symmetry x  = -b /2a  = -8/-2 = 4

Vertex 

f (x ) = -x ²+ 8x + 1

y = -(4)² + 8(4) + 1 = 17

Vertex  (x , y ) = (4, 17)

In this case a  < 0 parabola opens down.

f has maximum at x  = 4 and the maximum value is 17.

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for x and find the corresponding values for y.

x	y = -x 2 + 8x + 1	(x, y )
- 1	y = - (- 1)2+ 8 (- 1) + 1 = -1 - 8 + 1 = -8	(- 1, -8)
- 2	y = -(- 2)2 + 8 (- 2) + 1 = - 4 - 16 + 1 = -19	(- 2, -19)
0	y = -(0)2 + 8(0) + 1 =  1	(0, 1)
1	y = -(1)2 +8 (1) + 1 = -1 + 8 + 1 = 8	(1, 8)
2	y = -(2)2 + 8(2) + 1 = -4 + 16 + 1 = 13	(2, 13)

1.Draw a coordinate plane.

2.Plot the coordinate points.

3.Then sketch the graph, connecting the points with a smooth curve.

From the graph we can oberve the line of symmetry , maximum value , vertex of the quadratic function.