y= -x^2-8x-16

Question

I need to know whether the graph opens up or down, the axis of symmetry, the vertex, the y-intercept, the x-intercepts

Answer 1

Given equation y = -x^2-8x-16

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

a = -1, b = -8, c = -16

Axis of symmetry x = -b/2a

x = -(-8)/2*-1

x = -4

Substitute x value in given equation y = -16+32-16

y = 0

Vertex of given parabola = (-4,0)

To fnd x intercept substitute x = 0 n given equation.

y = -16

To find y intercept substitute y = 0 in given equation.

0 = -x^2-8x-16

Multiple to each side by negitive one.

x^2+8x+16 = 0

From the formula (a+b)^2 = a^2+2ab+b^2

(x+4)^2 = 0

x+4 = 0

x = -4

x, y intercepts are -4,-16.

Graph of parabola

Draw the coordinate plane.

Plot the vertex of parabola.

Draw the curve neatly with satsifying conditions of intercepts.

Formed parabola is indicating required graph of parabola.

Answer 2

The equation is f(x) = y = - x² - 8x - 16.

The standard form of a parabola equation is y = ax² + bx + c.

• The role of ' a '.

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

Compare the given equation with standard form of parabola equation.

a = - 1, b = - 8, and c = - 16.

a = - 1 (< 0), so the parabola opens downwards.

• The axis of symmetry is the line x = - b/2a.

The axis of symmetry x = - (- 8)/2(- 1) = - 4.

• The vertex (x, y) = (x, f(x))

= (- 4, f(- 4))

= (- 4, [ - (- 4)² - 8(- 4) - 16 ] )

= (- 4, 0).

The vertex (x, y) = (- 4, 0).

• To find y - intercept, substitute x = 0 in y = - x² - 8x - 16.

y = - 0² - 8(0) - 16

⇒ y = - 16.

The y - intercept of the parabola is - 16.

• To find x - intercept, substitute y = 0 in  y = - x² - 8x - 16.

- x² - 8x - 16 = 0

x² + 8x + 16 = 0

By factor by grouping.

x² + 4x + 4x + 16 = 0

x(x + 4) + 4(x + 4) = 0

(x + 4)² = 0

x + 4 = 0

⇒ x = - 4.

The x - intercept of the parabola is - 4.

•  

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 = - x2 - 8x - 16	(x, y)
- 8	y = -(-8)2-8(-8)-16 = -16	(- 8, - 16)
- 6	y = -(-6)2-8(-6)-16 = -4	(- 6, - 4)
- 4	y = -(-4)2-8(-4)-16 = 0	(- 4, 0)
- 2	y = -(-2)2-8(-2)-16 = -4	(- 2, - 4)
0	y = -(0)2-8(0)-16 = -16	(0, - 16)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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

Graph :