How do you graph a parabola with points?

To begin, we graph our first parabola by plotting points. Given a quadratic equation of the form y=ax2+bx+c y = a x 2 + b x + c , x is the independent variable and y is the dependent variable. Choose some values for x and then determine the corresponding y-values. Then plot the points and sketch the graph.

What is the equation of a parabola?

Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y – mx – b)^2 / (m^2 +1) = (x – h)^2 + (y – k)^2.

What is the general equation of parabola?

If a parabola has a vertical axis, the standard form of the equation of the parabola is this: (x – h)2 = 4p(y – k), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h, k + p).

How do you find the standard form of three points?

Use the standard form y=ax2+bx+c and the 3 points to write 3 equations with, a, b, and c as the variables and then solve for the variables.

What are the steps to graphing a parabola?

There are 3 main steps to graphing a parabola in standard form. STEP 1: Find the axis of symmetry STEP 2: Find the vertex STEP 3: Find two other points and reflect them across the line of symmetry. Then connect the five points with a smooth curve.

How do you determine the equation of a parabola?

In mathematical terms, a parabola is expressed by the equation f (x) = ax^2 + bx + c. Finding the midpoint between the parabola’s two x-intercepts gives you the x-coordinate of the vertex, which you can then substitute into the equation to find the y-coordinate as well.

How do you graph parabola?

Use the gray gridlines to graph your parabola, or draw your own horizontal and vertical lines inside the square. The line tool is located on the “Insert Shapes” panel in the far left of the “Drawing Tools” tab. If you draw your own lines, you can use the buttons on the “Shape Styles” panel to color them or change the line thickness.

How to write equations for a parabola?

Writing the Equation of Parabolas Determine which pattern to use (based on whether it is horizontal or vertical) Substitute in h and k Choose a coordinate to substitute in and solve for a. Write your final equation with a, h, and k.