solve and graph quadratic function. 2x^2-12x+11

Answer 1

The quadratic function is f(x) = y = 2x² - 12x + 11.

Solve the quadratic function by using quadratic formula.

2x² - 12x + 11 = 0.

Compare the above equation with he standard form of the quadratic equation.

Solution, x = [- b ± √(b² - 4ac)]/2a

a = 2, b = - 12, and c = 11.

x = [12 ± √(12² - 4*2*11)]/2*2

x = [12 ± √(144 - 88)]/4

x = [12 ± √56]/4

x = [12 ± 2√14]/4

x = [6 ± √14]/2.

The solutions of the given quadratic equation are x = [6 - √14]/2 and x = [6 + √14]/2.

Every quadratic function represents a parabola.

Graph of the parabola in vertex form :

The quadratic function is f(x) = y = 2x² - 12x + 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 parabola is f(x) = y = 2x² - 12x + 11.

Write the equation in vertex form of a parabola equation.

Divide each side by negative 2.

y/2 = x² - 6x + 11/2

To change the expression [x² - 6x + 11/2] 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 + 11/2 - 9

y/2 = (x - 3)² - 7/2.

y = 2(x - 3)² - 7.

Compare the equation y = 2(x - 3)² - 7 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) = (3, - 7), and axis of symmetry x = 3.

Answer 2

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 = 2(x - 3)2 - 7	(x, y)
0	y = 2(0 - 3)2 - 7 = 2(- 3)2 - 7 = 18 - 7 = 11	(0, 11)
1	y = 2(1 - 3)2 - 7 = 2(- 2)2 - 7 = 8 - 7 = 1	(1, 1)
2	y = 2(2 - 3)2 - 7 = 2(- 1)2 - 7 = 2 - 7 = - 5	(2, - 5)
3	y = 2(3 - 3)2 - 7 = 0 - 7 = - 7	(3, - 7)
4	y = 2(4 - 3)2 - 7 = 2(1)2 - 7 = 2 - 7 = - 5	(4, - 5)
5	y = 2(5 - 3)2 - 7 = 2(2)2 - 7 = 8 - 7 = 1	(5, 1)
6	y = 2(6 - 3)2 - 7 = 2(3)2 - 7 = 18 - 7 = 11	(6, 11)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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