Graph square root of 9x^2-65x+14

$\sqrt{9 x^{2} - 65 x + 14}$

Find the $y$ value at $x = 0$ .

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Replace the variable $x$ with $0$ in the expression.

$f (0) = \sqrt{(9 (0) - 2) ((0) - 7)}$

Simplify the result.

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Multiply $9$ by $0$ .

$f (0) = \sqrt{(0 - 2) ((0) - 7)}$

Subtract $2$ from $0$ .

$f (0) = \sqrt{- 2 ((0) - 7)}$

Subtract $7$ from $0$ .

$f (0) = \sqrt{- 2 \cdot - 7}$

Multiply $- 2$ by $- 7$ .

$f (0) = \sqrt{14}$

The final answer is $\sqrt{14}$ .

$\sqrt{14}$

The $y$ value at $x = 0$ is $\sqrt{14}$ .

$y = \sqrt{14}$

Find the $y$ value at $x = - 1$ .

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Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = \sqrt{(9 (- 1) - 2) ((- 1) - 7)}$

Simplify the result.

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Multiply $9$ by $- 1$ .

$f (- 1) = \sqrt{(- 9 - 2) ((- 1) - 7)}$

Subtract $2$ from $- 9$ .

$f (- 1) = \sqrt{- 11 ((- 1) - 7)}$

Subtract $7$ from $- 1$ .

$f (- 1) = \sqrt{- 11 \cdot - 8}$

Multiply $- 11$ by $- 8$ .

$f (- 1) = \sqrt{88}$

Rewrite $88$ as $2^{2} \cdot 22$ .

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Factor $4$ out of $88$ .

$f (- 1) = \sqrt{4 (22)}$

Rewrite $4$ as $2^{2}$ .

$f (- 1) = \sqrt{2^{2} \cdot 22}$

Pull terms out from under the radical.

$f (- 1) = 2 \sqrt{22}$

The final answer is $2 \sqrt{22}$ .

$2 \sqrt{22}$

The $y$ value at $x = - 1$ is $2 \sqrt{22}$ .

$y = 2 \sqrt{22}$

Find the $y$ value at $x = - 2$ .

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Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = \sqrt{(9 (- 2) - 2) ((- 2) - 7)}$

Simplify the result.

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Multiply $9$ by $- 2$ .

$f (- 2) = \sqrt{(- 18 - 2) ((- 2) - 7)}$

Subtract $2$ from $- 18$ .

$f (- 2) = \sqrt{- 20 ((- 2) - 7)}$

Subtract $7$ from $- 2$ .

$f (- 2) = \sqrt{- 20 \cdot - 9}$

Multiply $- 20$ by $- 9$ .

$f (- 2) = \sqrt{180}$

Rewrite $180$ as $6^{2} \cdot 5$ .

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Factor $36$ out of $180$ .

$f (- 2) = \sqrt{36 (5)}$

Rewrite $36$ as $6^{2}$ .

$f (- 2) = \sqrt{6^{2} \cdot 5}$

Pull terms out from under the radical.

$f (- 2) = 6 \sqrt{5}$

The final answer is $6 \sqrt{5}$ .

$6 \sqrt{5}$

The $y$ value at $x = - 2$ is $6 \sqrt{5}$ .

$y = 6 \sqrt{5}$

Find the $y$ value at $x = 7$ .

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Replace the variable $x$ with $7$ in the expression.

$f (7) = \sqrt{(9 (7) - 2) ((7) - 7)}$

Simplify the result.

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Multiply $9$ by $7$ .

$f (7) = \sqrt{(63 - 2) ((7) - 7)}$

Subtract $2$ from $63$ .

$f (7) = \sqrt{61 ((7) - 7)}$

Subtract $7$ from $7$ .

$f (7) = \sqrt{61 \cdot 0}$

Multiply $61$ by $0$ .

$f (7) = \sqrt{0}$

Rewrite $0$ as $0^{2}$ .

$f (7) = \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$f (7) = 0$

The final answer is $0$ .

$0$

The $y$ value at $x = 7$ is $0$ .

$y = 0$

Find the $y$ value at $x = 8$ .

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Replace the variable $x$ with $8$ in the expression.

$f (8) = \sqrt{(9 (8) - 2) ((8) - 7)}$

Simplify the result.

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Multiply $9$ by $8$ .

$f (8) = \sqrt{(72 - 2) ((8) - 7)}$

Subtract $2$ from $72$ .

$f (8) = \sqrt{70 ((8) - 7)}$

Subtract $7$ from $8$ .

$f (8) = \sqrt{70 \cdot 1}$

Multiply $70$ by $1$ .

$f (8) = \sqrt{70}$

The final answer is $\sqrt{70}$ .

$\sqrt{70}$

The $y$ value at $x = 8$ is $\sqrt{70}$ .

$y = \sqrt{70}$

Find the $y$ value at $x = 9$ .

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Replace the variable $x$ with $9$ in the expression.

$f (9) = \sqrt{(9 (9) - 2) ((9) - 7)}$

Simplify the result.

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Multiply $9$ by $9$ .

$f (9) = \sqrt{(81 - 2) ((9) - 7)}$

Subtract $2$ from $81$ .

$f (9) = \sqrt{79 ((9) - 7)}$

Subtract $7$ from $9$ .

$f (9) = \sqrt{79 \cdot 2}$

Multiply $79$ by $2$ .

$f (9) = \sqrt{158}$

The final answer is $\sqrt{158}$ .

$\sqrt{158}$

The $y$ value at $x = 9$ is $\sqrt{158}$ .

$y = \sqrt{158}$

List the points to graph.

$(0, 3.74165738), (- 1, 9.38083151), (- 2, 13.41640786), (7, 0), (8, 8.36660026), (9, 12.56980508)$

Select a few points to graph.

$\begin{array}{c} x & y \\ - 2 & 13.416 \\ - 1 & 9.381 \\ 0 & 3.742 \\ 7 & 0 \\ 8 & 8.367 \\ 9 & 12.57 \end{array}$

Graph square root of 9x^2-65x+14

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