y=−2x^2−12x−15

Question

how to graph it

Answer 1

Given equation y = -2x^2-12x-15

Compare it standard parabola equation y = ax^2+bx+c

To find coordinate pairs substitute x = -2,-3,-4 in given equation respectively,

Then the set of coordinate pair would be -1,3,1.

We can able to write the points are (-2,-1), (-3,3), (-4,1).

Graph of parabola

Draw the coordinate plane.

Plot the above points.

Connect the plotted points neatly lke a curve.

Then the formed parabola is indicating required parabola.

Answer 2

Graph of the parabola in vertex form :

The vertex form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h and

• The role of ' a '.

1. If a > 0, then the parabola opens upwards.
2. If a < 0, then the parabola opens downwards.

The parabola is f(x) = y = - 2x² - 12x - 15.

Write the equation in vertex form of a parabola eqaution.

Divide each side by negative 2.

- y/2 = x² + 6x + 15/2

To change the expression [x² + 6x + 15/2] into a perfect square trinomial add and subtract (half the x coefficient)²

 Here x coefficient = 6. so, (half the x coefficient)² = (6/2)²= 9.

Add and subtract 9 to the expression.

- y/2 = x² + 6x + 9 + 15/2 -  9

- y/2 = (x + 3)² - 3/2.

y = - 2(x + 3)² + 3.

Compare the equation - 2(x + 3)² + 3 with the vertex form of parabola equation.

Since a = - 2(< 0) the parabola opens downwards.

Vertex (h, k) = (- 3, 3), and axis of symmetry x = - 3.

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 = - 2(x + 3)2 + 3	(x, y)
- 5	y = - 2(- 5 + 3)2 + 3 = - 2(- 2)2 + 3 = - 8 + 3 = - 5	(- 5, - 5)
- 4	y = - 2(- 4 + 3)2 + 3 = - 2(- 1)2 + 3 = - 2 + 3 = 1	(- 4, 1)
- 3	y = - 2(- 3 + 3)2 + 3 = - 2(0)2 + 3 = 0 + 3 = 3	(- 3, 3)
- 2	y = - 2(- 2 + 3)2 + 3 = - 2(1)2 + 3 = - 2 + 3 = 1	(- 2, 1)
- 1	y = - 2(- 1 + 3)2 + 3 = - 2(2)2 + 3 = - 8 + 3 = - 5	(- 1, - 5)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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