y = -3x^2 - 6x - 5 Graph on coordinate plane

Question

Graph on a coordinate plane, label x & y intercepts, include ordered pair, label vertex as applicable (including ordered pair).

Answer 1

The equation is y  = -3x ² - 6x - 5

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

a  = - 3 , b  = -6 , c = -5.

Axis of symmetry x = -b /2a  = 6/-6 = -1.

To find vertex substiute x value in y = -3x ² - 6x - 5.

y = -3 + 6 - 5 = -2

Vertex = (-1, -2)

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 = -3x2 - 6x - 5	(x, y )
- 1	y = -3 (- 1)^2 -6 (- 1) -5 = -3 + 6 - 5 = -2	(- 1, -2)
- 2	y = -3(- 2)^2 -6 (- 2) - 5 = -12 +12 - 5 = -5	(- 2, -5)
0	y = -3(0)^2 -6 (0) - 5 = -5	(0, -5)
1	y = -3(1)^2 -6 (1) - 5 = -3 -6 -5 = -14	(1, -14)
2	y = -3(2)^2 -6 (2) - 5 = -12 -12 - 5 = -29	(2, -29)

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 observe vertex (x , y ) = (-1 , - 2)

There is no x  intercept of parabola.

y  - intercept is (0 ,-5).