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Which equation best matches the graph shown below?
Answer

y=-0.8x^(2)+x-6

y=0.8x^(2)+x-6.3

y=0.8x^(2)+x-6

y=-0.8x^(2)+x-6.3

Which equation best matches the graph shown below? $\newline$ Answer $\newline$ $y=-0.8 x^{2}+x-6$ $\newline$ $y=0.8 x^{2}+x-6.3$ $\newline$ $y=0.8 x^{2}+x-6$ $\newline$ $y=-0.8 x^{2}+x-6.3$

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Find derivatives of using multiple formulae

Full solution

Q. Which equation best matches the graph shown below?

\newline

Answer

\newline

y=-0.8 x^{2}+x-6

\newline

y=0.8 x^{2}+x-6.3

\newline

y=0.8 x^{2}+x-6

\newline

y=-0.8 x^{2}+x-6.3

Analyze graph shape: Step $1$ : Analyze the graph's shape to determine if it's an upward or downward parabola. If it opens downwards, the coefficient of $x^2$ should be negative.
Compare vertex and y-intercept: Step $2$ : Compare the vertex and y-intercept of the graph with the equations provided. Check if the y-intercept matches $-6$ or $-6.3$ .
Substitute known point: Step $3$ : Substitute a known point from the graph (other than the vertex or $y$ -intercept) into each equation to see which one fits.
Verify slope at vertex: Step $4$ : Verify the slope at the vertex by calculating the derivative of each equation and evaluating it at the vertex's $x$ -coordinate.
Confirm best matching equation: Step $5$ : Confirm the best matching equation based on the previous steps' results.

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