Question

question 4 of 10 step 1 of 1
for the following equation, determine the values of the missing entries. reduce all fractions to lowest terms.
( y = x^2 - 14x + 49 )
note: each column in the table represents an ordered pair. if multiple solutions exist, you only need to identify one.
answer 2 points
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table with x and y columns, x values: (blank), 6, (blank), 10, 5; y values: 0, (blank), 1, (blank), (blank)

Explanation:

Step1: Factor the quadratic equation

$y = x^2 -14x +49 = (x-7)^2$

Step2: Find x when y=0

Set $0=(x-7)^2$, solve for $x$:
$x-7=0 \implies x=7$

Step3: Find y when x=6

Substitute $x=6$:
$y=(6-7)^2=(-1)^2=1$

Step4: Find x when y=1

Set $1=(x-7)^2$, solve for $x$:
$x-7=\pm1 \implies x=8$ or $x=6$ (choose $x=8$)

Step5: Find y when x=10

Substitute $x=10$:
$y=(10-7)^2=(3)^2=9$

Step6: Find y when x=5

Substitute $x=5$:
$y=(5-7)^2=(-2)^2=4$

Answer:

$x$	$y$
6	1
8	1
10	9
5	4