# What is the derivative graph of a parabola?

## What is the derivative graph of a parabola?

Let the equation of the parabola will be y=ax2+bx+c. Hence the derivative graph of the parabola is Straight Line.

## What is the derivative of a graph?

The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where f(x) has a tangent line with positive slope, f′(x)>0.

**What is the first derivative of a parabola?**

Yes: the graph of a quadratic is a parabola, either opening upward or downward! For example, the 1st derivative of f(x) = 5×2 + 2x – 1 is 10x + 2. The 2nd derivative is simply 10, indicating concave up, for all values of x; and indeed f(x) is concave up everywhere—and its critical point is a local minimum.

### What is the graph of a parabola?

The graph of a quadratic function is a U-shaped curve called a parabola. The extreme point ( maximum or minimum ) of a parabola is called the vertex, and the axis of symmetry is a vertical line that passes through the vertex. The x-intercepts are the points at which the parabola crosses the x-axis.

### Which graph is the derivative of the top graph?

original function

Derivative Graph Rules The top graph is the original function, f(x), and the bottom graph is the derivative, f'(x).

**How do you find the derivative of a curve?**

The derivative of the parametrically defined curve x=x(t) and y=y(t) can be calculated using the formula dydx=y′(t)x′(t). Using the derivative, we can find the equation of a tangent line to a parametric curve.

#### What is the derivative of quadratic?

The derivative function of a quadratic function is a linear function. As Fermat already knew, at a local maximum or minimum the tangent is horizontal, the derivative is 0. We can see that at the vertex of a parabola the tangent is horizontal and that the derivative of the function cuts the x-axis at this value.