How do you find the area of a line and parabola?

Thus, the area between the x – axis and the parabola is \[\dfrac{8\sqrt{2}{{a}^{2}}}{3}\]. Therefore, the area between the straight line and parabola is given as the difference between the area under the line and the area under the parabola.

What is the bottom of a parabola?

The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point. The x-intercepts are called the roots, or the zeros.

How do you find the shaded area of a curve?

The area between two graphs can be found by subtracting the area between the lower graph and the x-axis from the area between the upper graph and the x-axis. Calculate the area shaded between the graphs y= x+2 and y = x2 .

What are the roots of a parabola?

The roots are the x-intercepts, where the parabola crosses the x-axis. If the parabola opens up and it’s vertex is below the x-axis then it crosses the x-axis in two places and has two (real) roots. If the vertex is on the x-axis then the parabola has one root.

How do you find the area of a graph?

To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive. This means that you have to be careful when finding an area which is partly above and partly below the x-axis.

How do you find the area under a graph in physics?

The area of a rectangle is determined by multiplying the base by the height. A = b • h where b = 4 s and h = 30 m/s. That is, the object was displaced 120 m during the first 4 seconds of motion. The area of a rectangle is determined by multiplying the base by the height.

What is the formula for a parabola area?

Parabola Formula: This computes the y coordinate of a parabola in the form y = a•x²+b•x+c

How do you plot a parabola?

Plot the parabola on the line graph. Plot the vertex, x-intercept and y-intercepts points on the graph with large dots. Connect the dots with one continuous u-shaped line and continue the lines to near the end of the graph. Draw an arrow at both ends of the parabola line to represent infinity.

How do you solve a parabola equation?

To graph a parabola, use the coefficient a and coefficient b values from your parabolic equation in the formula x = -b ÷ 2a to solve for x, which is the first coordinate of the vertex. Next, plug x back into your equation to solve for y, which is the second coordinate of the vertex.

How do you calculate the focus of a parabola?

The focus of a parabola from a given algebraic equation has a distance p from the curve’s vertex. To determine the location of the focus, the algebraic equation must be arranged in the form (x-h)^2 = 4p (y-k). From this form, one may extract the value of p and determine the coordinates of the focus.