Graph the function. \[ y=4 x^{2}-6 \]
Solution
Step 1 ：The function to be graphed is \(y=4x^{2}-6\).
Step 2 ：The x-axis represents the input values (x) and the y-axis represents the output values (y).
Step 3 ：We can use a range of x values and calculate the corresponding y values using the function \(y=4x^{2}-6\).
Step 4 ：The graph of the function \(y=4x^{2}-6\) is a parabola opening upwards with a vertex at \((0, -6)\).
Step 5 ：The graph is symmetric about the y-axis.
Step 6 ：The function is always increasing for \(x > 0\) and always decreasing for \(x < 0\).
Step 7 ：The minimum value of the function is \(-6\) which occurs at \(x = 0\).
Step 8 ：\(\boxed{\text{The graph of the function } y=4x^{2}-6 \text{ is a parabola opening upwards with a vertex at } (0, -6). \text{ The function is always increasing for } x > 0 \text{ and always decreasing for } x < 0. \text{ The minimum value of the function is } -6 \text{ which occurs at } x = 0.}\)
