Question

determine whether each point lies on the graph of the equation.
$y = x^2 - 7x + 6$
(a) $(6, 0)$
\\(\circ\\) yes, the point is on the graph.
\\(\circ\\) no, the point is not on the graph.
(b) $(-6, 82)$
\\(\circ\\) yes, the point is on the graph.
\\(\circ\\) no, the point is not on the graph.

Explanation:

Part (a)

Step1: Substitute \( x = 6 \) into the equation

We have the equation \( y = x^2 - 7x + 6 \). Substitute \( x = 6 \) into the right - hand side of the equation.
\( y=(6)^2-7\times(6)+6 \)

Step2: Calculate the value of \( y \)

First, calculate \( 6^2 = 36 \), \( 7\times6 = 42 \). Then:
\( y=36 - 42+6=0 \)
The \( y \) - value we get is equal to the \( y \) - coordinate of the point \( (6,0) \).

Step1: Substitute \( x=-6 \) into the equation

We have the equation \( y = x^2 - 7x + 6 \). Substitute \( x = - 6 \) into the right - hand side of the equation.
\( y=(-6)^2-7\times(-6)+6 \)

Step2: Calculate the value of \( y \)

First, calculate \( (-6)^2=36 \), \( - 7\times(-6) = 42 \). Then:
\( y=36 + 42+6=84 \)
The \( y \) - value we get (\( y = 84 \)) is not equal to the \( y \) - coordinate of the point \( (-6,82) \) (which is 82).

Answer:

Yes, the point is on the graph.

Part (b)