which quadratic function is represented by the table? \\(\\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline…

which quadratic function is represented by the table? \\(\\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline -2 & 21 \\\\ \\hline -1 & 10 \\\\ \\hline 0 & 5 \\\\ \\hline 1 & 6 \\\\ \\hline 2 & 13 \\\\ \\hline \\end{array}\\) \\(\\bigcirc\\ f(x) = 3x^2 + 2x - 5\\) \\(\\bigcirc\\ f(x) = 3x^2 - 2x + 5\\) \\(\\bigcirc\\ f(x) = 2x^2 + 3x - 5\\) \\(\\bigcirc\\ f(x) = 2x^2 - 2x + 5\\)

which quadratic function is represented by the table? \\(\\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline -2 & 21 \\\\ \\hline -1 & 10 \\\\ \\hline 0 & 5 \\\\ \\hline 1 & 6 \\\\ \\hline 2 & 13 \\\\ \\hline \\end{array}\\) \\(\\bigcirc\\ f(x) = 3x^2 + 2x - 5\\) \\(\\bigcirc\\ f(x) = 3x^2 - 2x + 5\\) \\(\\bigcirc\\ f(x) = 2x^2 + 3x - 5\\) \\(\\bigcirc\\ f(x) = 2x^2 - 2x + 5\\)

Answer

Explanation:

Step1: Test x=0 in all options

For $f(x)=3x^2 + 2x - 5$: $\quad 3(0)^2 + 2(0) - 5 = -5 \neq 5$ For $f(x)=3x^2 - 2x + 5$: $\quad 3(0)^2 - 2(0) + 5 = 5$ For $f(x)=2x^2 + 3x - 5$: $\quad 2(0)^2 + 3(0) - 5 = -5 \neq 5$ For $f(x)=2x^2 - 2x + 5$: $\quad 2(0)^2 - 2(0) + 5 = 5$ Eliminate first and third options.

Step2: Test x=1 in remaining options

For $f(x)=3x^2 - 2x + 5$: $\quad 3(1)^2 - 2(1) + 5 = 3 - 2 + 5 = 6$ For $f(x)=2x^2 - 2x + 5$: $\quad 2(1)^2 - 2(1) + 5 = 2 - 2 + 5 = 5 \neq 6$ Eliminate fourth option.

Step3: Verify with x=2

For $f(x)=3x^2 - 2x + 5$: $\quad 3(2)^2 - 2(2) + 5 = 12 - 4 + 5 = 13$ Matches the table value.

Answer:

B. $f(x)=3x^2 - 2x + 5$