How do you find the equation of a parabola given the vertex and a point?

We can use the vertex form to find a parabola’s equation. The idea is to use the coordinates of its vertex (maximum point, or minimum point) to write its equation in the form y=a(x−h)2+k (assuming we can read the coordinates (h,k) from the graph) and then to find the value of the coefficient a.

What is the equation of the parabola with vertical axis of symmetry and vertex H K?

To graph parabolas with a vertex (h,k) other than the origin, we use the standard form (y−k)2=4p(x−h) ( y − k ) 2 = 4 p ( x − h ) for parabolas that have an axis of symmetry parallel to the x-axis, and (x−h)2=4p(y−k) ( x − h ) 2 = 4 p ( y − k ) for parabolas that have an axis of symmetry parallel to the y-axis.

What is the standard form of the equation of a parabola with a vertical axis of symmetry?

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).

What is the equation for parabola?

Parabola Equation The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.

How do you find the equation of the axis of symmetry of the parabola?

If the vertex of a parabola is (k,l), then its axis of symmetry has equation x=k. We can find a simple formula for the value of k in terms of the coefficients of the quadratic. As usual, we complete the square: y=ax2+bx+c=a[x2+bax+ca]=a[(x+b2a)2+ca−(b2a)2].

What is the vertex of a parabola?

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. In this equation, the vertex of the parabola is the point (h,k) .

How do you find the equation of a parabola from a graph?

Key Takeaways

1. The graph of any quadratic equation y=ax2+bx+c y = a x 2 + b x + c , where a, b, and c are real numbers and a≠0 a ≠ 0 , is called a parabola.
2. When graphing parabolas, find the vertex and y-intercept.
3. Use the leading coefficient, a, to determine if a parabola opens upward or downward.

What is the equation for a parabola graph?

Parabola Graph Parabola is a curve and whose equation is in the form of f (x) = ax2+bx+c, which is the standard form of a parabola. To draw a parabola graph, we have to first find the vertex for the given equation. This can be done by using x=-b/2a and y = f (-b/2a).

This high or low point is called the vertex of the graph. The parabola is symmetric about a vertical line, called the axis of symmetry, that runs through the vertex. The y y -intercept is the point where the parabola intersects the y y -axis.

How do you find the axis of symmetry of a parabola?

If the value of a is greater than 0 (a>0), then the parabola graph is oriented towards the upward direction. If the value of a is less than 0 (a<0), then the parabola graph opens downwards. The axis of symmetry from the standard form of the parabola equation is given as x= -b/2a.

How many points are needed to draw a parabola?

We need to determine at least five points as a medium to design a pleasing shape. In the beginning, we draw a parabola by plotting the points. Suppose we have a quadratic equation of the form y=ax 2 + bx+c, where x is the independent variable and y is the dependent variable.