Questions: Graph the equation by hand by plotting points. Verify your results using a graphing utility. y=-x^2+15

Transcript text: Graph the equation by hand by plotting points. Verify your results using a graphing utility. \[ y=-x^{2}+15 \]

Solution

Solution Steps

Step 1: Identify the Equation

The given equation is: \[ y = -x^2 + 15 \]

Step 2: Determine Key Points

To graph the equation, we can determine key points by substituting values for $x$ and solving for $y$.

When $x = 0$, $y = -0^2 + 15 = 15$.
When $x = 1$, $y = -(1)^2 + 15 = 14$.
When $x = -1$, $y = -(-1)^2 + 15 = 14$.
When $x = 2$, $y = -(2)^2 + 15 = 11$.
When $x = -2$, $y = -(-2)^2 + 15 = 11$.

Step 3: Plot the Points

Plot the points $(0, 15)$, $(1, 14)$, $(-1, 14)$, $(2, 11)$, and $(-2, 11)$ on a Cartesian coordinate system.

Final Answer

The equation $y = -x^2 + 15$ is a downward-opening parabola with its vertex at $(0, 15)$.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": 0, "ymax": 16}, "commands": ["y = -x**2 + 15"], "latex_expressions": ["$y = -x^2 + 15$"]}

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