Question

P A student is asked to find the x-intercepts for the equation y = 2x^2

2x2 – 16x + 14 by completing the square.

Answer 1

The x-intercepts of the equation y = 2x^2 - 16x + 14 are found by completing the square and solving the resulting equation, which gives the intercepts at (1,0) and (7,0).

Step-by-step explanation:

The student is asked to find the x-intercepts for the quadratic equation y = 2x^2 - 16x + 14 by completing the square. To find the x-intercepts, we set y to zero and rearrange the terms to facilitate completing the square:

1. Divide all terms by the leading coefficient 2 to simplify: x^2 - 8x + 7 = 0.
2. Move the constant term to the other side: x^2 - 8x = -7.
3. Add the value (b/2)^2 = (8/2)^2 = 16 to both sides to complete the square: x^2 - 8x + 16 = 9.
4. Now we have a perfect square on the left: (x - 4)^2 = 9.
5. Take the square root of both sides: x - 4 = ±3.
6. Solve for x: x = 4 ± 3, so the solutions are x = 7 and x = 1.

These solutions represent the x-intercepts of the quadratic equation, which are (1,0) and (7,0).

Answer 2

To find the x-intercepts of the equation y = 2x^2 - 2x^2 - 16x + 14 by completing the square, rearrange the equation, divide by the coefficient of x^2, complete the square, and solve for x.

Step-by-step explanation:

To find the x-intercepts of the equation y = 2x^2 - 2x^2 - 16x + 14 by completing the square, follow these steps:

1. Rearrange the equation to equal 0: 2x^2 - 16x + 14 = 0
2. Divide the equation by the coefficient of x^2 to make it easier to work with: x^2 - 8x + 7 = 0
3. Complete the square by adding and subtracting half the coefficient of x, squared: (x - 4)^2 - 9 = 0
4. Now, solve for x by taking the square root of both sides and adding and subtracting 4: x - 4 = ±3
5. Simplify each equation: x = 7 or x = 1

Therefore, the x-intercepts of the equation y = 2x^2 - 2x^2 - 16x + 14 are x = 7 and x = 1.