y=x²
quadratic parent function
The equation y = x² represents a parabolic function. When graphed, it will form a symmetric U shape. The vertex of the parabola is located at the origin (0,0) and the arms of the parabola extend upwards and downwards infinitely.
The x-axis intercepts can be found by plugging in y=0 and solving for x:
0 = x²
x = 0
Therefore, there is only one x-intercept, which is at the origin (0,0).
The y-axis intercept can be found by plugging in x=0 and solving for y:
y = 0²
y = 0
Therefore, the y-intercept is also at the origin (0,0).
The function is symmetric about the y-axis as well, which means that if we plug in a negative value for x, we’ll get the same y-value as its positive counterpart.
The domain of this function is all real numbers, which means that x can take on any value.
The range of this function is all non-negative y-values (y≥0), because the parabola opens upwards and never dips below the x-axis.
The function is differentiable at every point, which means that its derivative exists and can be calculated using the power rule:
f'(x) = 2x
The derivative gives us the slope of the tangent line at any point on the curve.
Finally, this function is commonly used to model various real-life phenomena, from the trajectory of a projectile to the shape of a satellite dish.
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