stuck on these also

Question

Find the vertex of the parabola

x coordinate = y coordinate =  
Graph this function and estimate the x intercepts to the nearest tenth. Give your answers in order. 
x intercept one = x intercept two = 

 

Answer 1

The parabola equation y = x²  + 8x - 9

Compare it to parabola equation y = ax²  + bx + c.

a = 1, b = 8, c = - 9

Axis of symmetry x = - b/2a

x = - 8/2(1)

x = - 4

Substitute x = - 4 in y = x²  + 8x - 9

y = (- 4)²  + 8(- 4) - 9

y =  - 25

Vertex of parabola is (x, y) = (- 4, - 25).

To find x intercepts substitute y = 0 in y = x²  + 8x - 9.

x²  + 8x - 9 = 0

Solve the equation for x.

x²  + 9x - x - 9 = 0

x ( x + 9) - 1(x + 9) = 0

(x + 9)(x - 1) = 0

x + 9 = 0 and x + 1 = 0

x intercepts are x = - 9 and  1

To graph the function we need some more points to accurate graph.

y	y = x2  + 8x - 9	(x, y)
-1	y=(-1)2+8(-1)-9	(-1,-16)
-6	y=(-6)2+8(-6)-9	(-6,-21)
1	y=(1)2+8(1)-9	(1,0)
3	y = (3)2+8(3)-9	(3,24)

Graph

Draw a coordinate plane.

Plot the vertex and axis of symmetry.

Plot the x intercepts, points found in the table.

Connect the points with smooth curve.

Vertex of parabola is (x, y) = (- 4, - 25).

x coordinate is -4 y coordinate is - 25

x intercept is -9 and x intercept is 1.