i need a graph

Question

y= -2x^2 + 12x - 10 give the vertex, x intercepts , y intercepts and symmetry also give the coordinates and all the intercepts and equation of the axis.

Answer 1

  

The parabola equation y = - 2x² + 12x - 10

y = - 2x² + 12x - 10

Compare it to y = ax² + bx + c

a = - 2, b = 12, c = - 10

Axis of symmetry x = -b/2a

x = -12/2(-2)

x = (- 12)/(-4)

x = 3

Equation of the axis x = 3.

3 is x coordinate of vertex.

To find y coordinate of vertex substitute x = 3 in y = - 2x² + 12x - 10.

y = - 2(3)² + 12(3) - 10

y = - 18 + 36 - 10

y = 8

Vertex (x, y) = ( 3, 8)

To find x intercept substitute y = 0 in y = - 2x² + 12x - 10

0 = - 2x² + 12x - 10

x² - 6x + 5 = 0

x² - 5x - x + 5 = 0

x(x - 5) - 1(x - 5) = 0

(x - 5)(x - 1) = 0

x = 5 and x = 1

x intercepts are 1 and 5.

To find y intercept substitute x = 0 in y = - 2x² + 12x - 10.

y = - 2(0)² + 12(0) - 10

y = - 10

y intercept is - 10.

Comments

Contd...

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

x	y  = -2x2+12x- 10	(x, y)
0	y =-2(0)2+12(0)-10	(0, -10)
2	y =-2(2)2+12(2)-10	(2, 6)
4	y =-2(4)2+12(4)-10	(4, 6)
6	y =-2(6)2+12(6)-10	(6, -10)
2	y = 3(2)2 - 7(2) + 4	(2, 2)

Graph

Draw the coordinate plane.

Plot axis of symmetry and the points found in the table, x, y intercepts.

Connect the plotted points with smooth curve.