graph the parabola y=x^2+6x

Question

graphing a parabola

Answer 1

Given y = x^2+6x

Compare y = ax^2+bx+c

a = 1, b = 6, c = 0

x = -b/2a

x = -6/2*1 = -3

Substitute x = -3 in y = x^2+6x

y = 9-18

y = -9

Vertex of parabola = (-3,-9)

Graph of parabola

Draw the coordinate plane.

observe from the graph axis of symmetry and vertex of parabola.

Answer 2

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

The parabola is y = x² + 6x.

Wrote the equation in standard form of a parabola eqaution.

To change the expression [x² + 6x] 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.

y = x² + 6x + 9 - 9

y = (x + 3)² - 9.

Compare the equation y = (x + 3)² - 9 with the standard form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h.

Vertex (h, k) = (- 3, - 9), 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 = (x + 3)2 - 9	(x, y)
- 7	y = (- 7 + 3)2 - 9 = (- 4)2 - 9 = 16 - 9 = 7	(- 7, 7)
- 6	y = (- 6 + 3)2 - 9 = (- 3)2 - 9 = 9 - 9 = 0	(- 6, 0)
- 5	y = (- 5 + 3)2 - 9 = (- 2)2 - 9 = 4 - 9 = - 5	(- 5, - 5)
- 4	y = (- 4 + 3)2 - 9 = (- 1)2 - 9 = 1 - 9 = - 8	(- 4, - 8)
- 3	y = (- 3 + 3)2 - 9 = (0)2 - 9 = 0 - 9 = - 9	(- 3, - 9)
- 2	y = (- 2 + 3)2 - 9 = (1)2 - 9 = 1 - 9 = - 8	(- 2, - 8)
- 1	y = (- 1 + 3)2 - 9 = (2)2 - 9 = 4 - 9 = - 5	(- 1, - 5)
0	y = (0 + 3)2 - 9 = (3)2 - 9 = 9 - 9 = 0	(0, 0)
1	y = (1 + 3)2 - 9 = (4)2 - 9 = 16 - 9 = 7	(1, 7)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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