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$Three points on the graph of the function f(x) are {(0,1),(1,4),(2,9)}. Which equation represents f(x) ? f(x)=5x-1 f(x)=4^(x) f(x)=(x+1)^(2) f(x)=3x+1$

Three points on the graph of the function $f(x)$ are $\{(0,1),(1,4),(2,9)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=5 x-1$ $\newline$ $f(x)=4^{x}$ $\newline$ $f(x)=(x+1)^{2}$ $\newline$ $f(x)=3 x+1$

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Math Problems

Algebra 1

Write a quadratic function from its x-intercepts and another point

Full solution

Q. Three points on the graph of the function

f(x)

are

\{(0,1),(1,4),(2,9)\}

. Which equation represents

f(x)

\newline

f(x)=5 x-1

\newline

f(x)=4^{x}

\newline

f(x)=(x+1)^{2}

\newline

f(x)=3 x+1

Test Equation $f(x)$ : Test the first equation $f(x) = 5x - 1$ with the given points. $\newline$ Substitute $x = 0$ into $f(x) = 5x - 1$ to see if it gives $y = 1$ . $\newline$ $f(0) = 5(0) - 1 = -1$ $\newline$ Check if this matches the given point $(0,1)$ .
Check $f(x) = 5x - 1$ : Since $f(0) = -1$ does not match the given point $(0,1)$ , we can conclude that $f(x) = 5x - 1$ is not the correct equation.
Test Equation $f(x)$ : Test the second equation $f(x) = 4^{x}$ with the given points. $\newline$ Substitute $x = 0$ into $f(x) = 4^{x}$ to see if it gives $y = 1$ . $\newline$ $f(0) = 4^{0} = 1$ $\newline$ Check if this matches the given point $(0,1)$ .
Check $f(x) = 4^{x}$ : Since $f(0) = 1$ matches the given point $(0,1)$ , we proceed to test the next point $(1,4)$ . Substitute $x = 1$ into $f(x) = 4^{x}$ to see if it gives $y = 4$ . $f(1) = 4^{1} = 4$ Check if this matches the given point $(1,4)$ .
Test Equation $f(x)$ : Since $f(1) = 4$ matches the given point $(1,4)$ , we proceed to test the last point $(2,9)$ . $\newline$ Substitute $x = 2$ into $f(x) = 4^{x}$ to see if it gives $y = 9$ . $\newline$ $f(2) = 4^{2} = 16$ $\newline$ Check if this matches the given point $(2,9)$ .
Check $f(x) = (x + 1)^{2}$ : Since $f(2) = 16$ does not match the given point $(2,9)$ , we can conclude that $f(x) = 4^{x}$ is not the correct equation.
Check $f(x) = (x + 1)^{2}$ : Since $f(2) = 16$ does not match the given point $(2,9)$ , we can conclude that $f(x) = 4^{x}$ is not the correct equation.Test the third equation $f(x) = (x + 1)^{2}$ with the given points. $\newline$ Substitute $x = 0$ into $f(x) = (x + 1)^{2}$ to see if it gives $y = 1$ . $\newline$ $f(0) = (0 + 1)^{2} = 1$ $\newline$ Check if this matches the given point $(0,1)$ .
Check $f(x) = (x + 1)^{2}$ : Since $f(2) = 16$ does not match the given point $(2,9)$ , we can conclude that $f(x) = 4^{x}$ is not the correct equation.Test the third equation $f(x) = (x + 1)^{2}$ with the given points. $\newline$ Substitute $x = 0$ into $f(x) = (x + 1)^{2}$ to see if it gives $y = 1$ . $\newline$ $f(0) = (0 + 1)^{2} = 1$ $\newline$ Check if this matches the given point $(0,1)$ .Since $f(2) = 16$ $0$ matches the given point $(0,1)$ , we proceed to test the next point $f(2) = 16$ $2$ . $\newline$ Substitute $f(2) = 16$ $3$ into $f(x) = (x + 1)^{2}$ to see if it gives $f(2) = 16$ $5$ . $\newline$ $f(2) = 16$ $6$ $\newline$ Check if this matches the given point $f(2) = 16$ $2$ .
Check $f(x) = (x + 1)^{2}$ : Since $f(2) = 16$ does not match the given point $(2,9)$ , we can conclude that $f(x) = 4^{x}$ is not the correct equation.Test the third equation $f(x) = (x + 1)^{2}$ with the given points. $\newline$ Substitute $x = 0$ into $f(x) = (x + 1)^{2}$ to see if it gives $y = 1$ . $\newline$ $f(0) = (0 + 1)^{2} = 1$ $\newline$ Check if this matches the given point $(0,1)$ .Since $f(2) = 16$ $0$ matches the given point $(0,1)$ , we proceed to test the next point $f(2) = 16$ $2$ . $\newline$ Substitute $f(2) = 16$ $3$ into $f(x) = (x + 1)^{2}$ to see if it gives $f(2) = 16$ $5$ . $\newline$ $f(2) = 16$ $6$ $\newline$ Check if this matches the given point $f(2) = 16$ $2$ .Since $f(2) = 16$ $8$ matches the given point $f(2) = 16$ $2$ , we proceed to test the last point $(2,9)$ . $\newline$ Substitute $(2,9)$ $1$ into $f(x) = (x + 1)^{2}$ to see if it gives $(2,9)$ $3$ . $\newline$ $(2,9)$ $4$ $\newline$ Check if this matches the given point $(2,9)$ .
Check $f(x) = (x + 1)^{2}$ : Since $f(2) = 16$ does not match the given point $(2,9)$ , we can conclude that $f(x) = 4^{x}$ is not the correct equation.Test the third equation $f(x) = (x + 1)^{2}$ with the given points. $\newline$ Substitute $x = 0$ into $f(x) = (x + 1)^{2}$ to see if it gives $y = 1$ . $\newline$ $f(0) = (0 + 1)^{2} = 1$ $\newline$ Check if this matches the given point $(0,1)$ .Since $f(2) = 16$ $0$ matches the given point $(0,1)$ , we proceed to test the next point $f(2) = 16$ $2$ . $\newline$ Substitute $f(2) = 16$ $3$ into $f(x) = (x + 1)^{2}$ to see if it gives $f(2) = 16$ $5$ . $\newline$ $f(2) = 16$ $6$ $\newline$ Check if this matches the given point $f(2) = 16$ $2$ .Since $f(2) = 16$ $8$ matches the given point $f(2) = 16$ $2$ , we proceed to test the last point $(2,9)$ . $\newline$ Substitute $(2,9)$ $1$ into $f(x) = (x + 1)^{2}$ to see if it gives $(2,9)$ $3$ . $\newline$ $(2,9)$ $4$ $\newline$ Check if this matches the given point $(2,9)$ .Since $(2,9)$ $6$ matches the given point $(2,9)$ , we can conclude that $f(x) = (x + 1)^{2}$ is the correct equation that represents $(2,9)$ $9$ .