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Three points on the graph of the function $f(x)$ are $(0,1)$ $(1,2)$ and $(2,4)$ which represents $f(x)$

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Find the vertex of a parabola

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Q. Three points on the graph of the function

f(x)

are

(0,1)

(1,2)

and

(2,4)

which represents

f(x)

Assume Linear Function: We will assume that the function $f(x)$ is linear since we have only $3$ points and a linear function is determined by $2$ points. We will use the two-point formula to find the equation of the line.
Calculate Slope: The two-point formula for a line is given by $(y - y_1) = m(x - x_1)$ , where $m$ is the slope of the line and $(x_1, y_1)$ is a point on the line.
Write Equation of Line: First, we calculate the slope $m$ using the points $(0,1)$ and $(1,2)$ . The slope $m$ is given by the change in $y$ divided by the change in $x$ , so $m = (2 - 1) / (1 - 0) = 1/1 = 1$ .
Verify Third Point: Now we use the slope $m = 1$ and one of the points, say $(0,1)$ , to write the equation of the line. Substituting into the two-point formula, we get $(y - 1) = 1(x - 0)$ , which simplifies to $y = x + 1$ .
Identify Math Error: We need to verify that the third point $(2,4)$ satisfies the equation $y = x + 1$ . Substituting $x = 2$ into the equation, we get $y = 2 + 1 = 3$ . However, the $y$ -coordinate of the third point is $4$ , not $3$ . This means there is a math error in our assumption that the function is linear.

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