graph the equation.

\y = -x^2 + 2x + 7\

first plot the solutions of the equation for the given values of $x$, and then connect the points with a smooth curve.

$x = -2, -1, 0, 1, 2, 3, 4$

\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
3 & \\
\hline
4 & \\
\hline
\end{array}

Question

graph the equation.

\y = -x^2 + 2x + 7\

first plot the solutions of the equation for the given values of $x$, and then connect the points with a smooth curve.

$x = -2, -1, 0, 1, 2, 3, 4$

\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
3 & \\
\hline
4 & \\
\hline
\end{array}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Quadratic Functions", "Function Evaluation" ], "new_concepts": [ "Graphing Quadratic Equations" ], "current_concepts": [ "Quadratic Functions", "Function Evaluation", "Graphing Quadratic Equations" ] } ## Evaluate the function at negative values Using the *Function Evaluation* and *Quadratic Functions* knowledge points $$ \begin{aligned} x = -2: \quad y &= -(-2)^2 + 2(-2) + 7 = -4 - 4 + 7 = -1 \ x = -1: \quad y &= -(-1)^2 + 2(-1) + 7 = -1 - 2 + 7 = 4 \end{aligned} $$ ## Evaluate the function at zero and positive values Using the *Function Evaluation* and *Quadratic Functions* knowledge points $$ \begin{aligned} x = 0: \quad y &= -(0)^2 + 2(0) + 7 = 7 \ x = 1: \quad y &= -(1)^2 + 2(1) + 7 = -1 + 2 + 7 = 8 \ x = 2: \quad y &= -(2)^2 + 2(2) + 7 = -4 + 4 + 7 = 7 \ x = 3: \quad y &= -(3)^2 + 2(3) + 7 = -9 + 6 + 7 = 4 \ x = 4: \quad y &= -(4)^2 + 2(4) + 7 = -16 + 8 + 7 = -1 \end{aligned} $$ | $x$ | $y$ | |---|---| | $-2$ | $-1$ | | $-1$ | $4$ | | $0$ | $7$ | | $1$ | $8$ | | $2$ | $7$ | | $3$ | $4$ | | $4$ | $-1$ | { "elements": [ { "type": "functiongraph", "params": [{"js": "-x*x + 2*x + 7", "latex": "-x^2 + 2x + 7"}, -3, 5], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [[-2, -1]], "properties": { "name": "(-2, -1)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[-1, 4]], "properties": { "name": "(-1, 4)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[0, 7]], "properties": { "name": "(0, 7)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[1, 8]], "properties": { "name": "(1, 8)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[2, 7]], "properties": { "name": "(2, 7)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[3, 4]], "properties": { "name": "(3, 4)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[4, -1]], "properties": { "name": "(4, -1)", "size": 4, "color": "#F2557F", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Quadratic Equations" ] }

\(x\)	\(y\)
\(-1\)	\(4\)
\(0\)	\(7\)
\(1\)	\(8\)
\(2\)	\(7\)
\(3\)	\(4\)
\(4\)	\(-1\)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate the function at negative values

Evaluate the function at zero and positive values

Answer: