Question

For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms. y = x2 - 4x + 4 Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one. Answer -1 y 0 I

Answer 1

To find the values of the missing entries for the equation y = x² - 4x + 4, substitute different values of x into the equation and solve for y. The ordered pairs for the equation are (-1, 9) and (0, 4).

Step-by-step explanation:

To find the values of the missing entries for the equation y = x² - 4x + 4, we can substitute different values of x into the equation and solve for y. Let's substitute -1 and 0 for x:

For x = -1, y = (-1)² - 4(-1) + 4 = 1 + 4 + 4 = 9

For x = 0, y = (0)² - 4(0) + 4 = 0 + 0 + 4 = 4

Therefore, the ordered pairs for the equation y = x² - 4x + 4 are (-1, 9) and (0, 4).

Answer 2

The values of the missing entries in the table can be expressed as:

x 2 1 3 5 0

y 0 1 1 9 4

Solving quadratic equations

In this question, we have a quadratic equation: y = x² - 4x + 4 and we are given the table of values in which we are to find some missing values from the table.

x 1 5 0

y 0 1

To find the value of x, we need to replace the equation with the value of y and vice versa.

When y = 0

y = x² - 4x + 4

x² - 4x + 4 = 0

(x - 2) (x -2) = 0

x = 2 (twice)

when x = 1

y = x² - 4x + 4

y = (1)² - 4(1) + 4

y = 1 - 4 + 4

y = 1

when y = 1

y = x² - 4x + 4

1 = x² - 4x + 4

x² - 4x + 4 - 1 = 0

x² - 4x + 3 = 0

(x - 3) (x - 1) = 0

x = 3 or 1

x = 3

when x = 5

y = x² - 4x + 4

y = (5)² - 4(5) + 4

y = 25 - 20 + 4

y = 9

when x = 0

y = x² - 4x + 4

y = (0)² - 4(0) + 4

y = 4

Therefore, the values of the missing entries in the table can be expressed as:

x 2 1 3 5 0

y 0 1 1 9 4