Questions: Graphs and Functions Graphing a function of the form f(x)=a x^2+c Graph the function. h(x)=3 x^2-4

Transcript text: Graphs and Functions Graphing a function of the form $f(x)=a x^{2}+c$ Graph the function. \[ h(x)=3 x^{2}-4 \]

Solution

Solution Steps

Step 1: Identify the Function

The function given is $ h(x) = 3x^2 - 4 $.

Step 2: Calculate Points

To plot the function, we need to calculate the values of $ h(x) $ for specific $ x $ values. Let's calculate for $ x = 0 $, $ x = 1 $, and $ x = -1 $.

For $ x = 0 $: \[ h(0) = 3(0)^2 - 4 = -4 \] Point: $ (0, -4) $
For $ x = 1 $: \[ h(1) = 3(1)^2 - 4 = 3 - 4 = -1 \] Point: $ (1, -1) $
For $ x = -1 $: \[ h(-1) = 3(-1)^2 - 4 = 3 - 4 = -1 \] Point: $ (-1, -1) $

Step 3: Additional Points

To ensure a smooth curve, calculate two more points, for example, $ x = 2 $ and $ x = -2 $.

For $ x = 2 $: \[ h(2) = 3(2)^2 - 4 = 12 - 4 = 8 \] Point: $ (2, 8) $
For $ x = -2 $: \[ h(-2) = 3(-2)^2 - 4 = 12 - 4 = 8 \] Point: $ (-2, 8) $

Final Answer

The points to plot are $ (0, -4) $, $ (1, -1) $, $ (-1, -1) $, $ (2, 8) $, and $ (-2, 8) $.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -5, "ymax": 10}, "commands": ["y = 3x^2 - 4"], "latex_expressions": ["$y = 3x^2 - 4$"]}

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