solve

Question

9)  Solve 2x2

 

 - 4x - 5 = 0 by completing the square.

 

10)  Use the quadratic formula to solve 7x2

 

 + x + 1 = 0.

 

11)  Identify the vertex point, axis of symmetry, x intercept and y intercept and graph the 

 

function:  y = x2

 

 + 2x – 15.

Answer 1

9)

2x^2 - 4x - 5 = 0

2(x^2 -2x) - 5 = 0

To change the equation (x^2 -2x)  into a perfect square trinomial,

add  and subtract (half of the x coefficient)²  .

2(x^2 -2x) - 5 = 0

2(x^2 -2x+1-1) - 5 = 0

2((x - 1)^2-1) - 5 = 0

Add 5 to eqch side.

2((x - 1)^2-1) - 5+5 = 0+5

2((x - 1)^2-1) = 5

(x - 1)^2-1 = 5/2

Add 1 to each side.

(x - 1)^2- 1 + 1 = 5/2 + 1

(x - 1)^2 = 7/2

x - 1 = ± √(7/2)

x = 1  ± √(7/2)

 

Answer 2

10)

7x^2+ x + 1 = 0.

Solve quadratic equation by using quadratic formula:

Answer 3

11).

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

The function is y = x² + 2x - 15.

Write the equation in vertex form of a parabola eqaution.

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

 Here x coefficient = 2 so, (half the x coefficient)² = (2/2)²= 1.

y = x² + 2x + 1 - 15 - 1

y = (x + 1)² - 16.

y = (x + 1)² - 16.

Compare the equation y = (x + 1)² - 16 with the vertex form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h.

Vertex (h, k) = (- 1, - 16), and axis of symmetry x = - 1.

Find the x - intercept, by substitute y = 0 in y = (x + 1)² - 16.

0 = (x + 1)² - 16

(x + 1)² = 16

x + 1 = (± 4)²

x + 1 = - 4  and  x + 1 = 4

x = - 4 - 1  and x = 4 - 1

x = - 5  and  x = 3.

Therefore, x - intercepts are (- 5, 0) and (3, 0).

Find the y - intercept, by substitute x = 0 in y = (x + 1)² - 16.

y = (0 + 1)² - 16

y = 1 - 16

y = - 15.

Therefore, y - intercept is (0, - 15).

 

Answer 4

Contd......

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 + 1)2 - 16	(x, y)
- 4	y = (- 4 + 1)2 - 16 = (- 3)2 - 16 = 9 - 16 = - 7	(- 4, - 7)
- 3	y = (- 3 + 1)2 - 16 = (- 2)2 - 16 = 4 - 16 = - 12	(- 3, - 12)
- 2	y = (- 2 + 1)2 - 16 = (- 1)2 - 16 = 1 - 16 = - 15	(- 2, - 15)
- 1	y = (- 1 + 1)2 - 16 = 0 - 16 = - 16	(- 1, - 16)
0	y = (0 + 1)2 - 16 = 1 - 16 =  - 15	(0, - 15)
1	y = (1 + 1)2 - 16 = (2)2 - 16 = 4 - 16 = - 12	(1, - 12)
2	y = (2 + 1)2 - 16 = (3)2 - 16 = 9 - 16 = - 7	(2, - 7)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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