How do you find the a value of a parabola given 2 points?

2 Answers By Expert Tutors

1. Using the vertex form of a parabola f(x) = a(x – h)2 + k where (h,k) is the vertex of the parabola.
2. The axis of symmetry is x = 0 so h also equals 0.
3. a = 1.
4. Substituting the a value into the first equation of the linear system:
5. k = 3.
6. f(1) = 4 = (1 – 0)2 + 3 = 1 + 3.
7. f(2) = 7 = (2 – 0)2 + 3 = 4 + 3.

How do you find the points of a quadratic equation?

We find the vertex of a quadratic equation with the following steps:

1. Get the equation in the form y = ax2 + bx + c.
2. Calculate -b / 2a. This is the x-coordinate of the vertex.
3. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.

What is K in parabola?

(h, k) is the vertex of the parabola, and x = h is the axis of symmetry. • the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). • the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

How do you find K in a parabola?

For a given quadratic y = ax2 + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k.

How do you write the quadratic equation of a parabola?

But, to make sure you’re up to speed, a parabola is a type of U-Shaped curve that is formed from equations that include the term x 2 x^{2} x2. Oftentimes, the general formula of a quadratic equation is written as: y = ( x − h ) 2 + k y = (x-h)^{2} + k y=(x−h)2+k.

How do you find the point and shape of a parabola?

Given y = ax2+ bx + c , we have to go through the following steps to find the points and shape of any parabola: Label a, b, and c. Decide the direction of the paraola: If a > 0 (positive) then the parabola opens upward.

Which way does the first parabola open?

We say that the first parabola opens upwards (is a U shape) and the second parabola opens downwards (is an upside down U shape). In order to graph a parabola we need to find its intercepts, vertex, and which way it opens. Given y = ax2+ bx + c , we have to go through the following steps to find the points and shape of any parabola:

How do you find the x intercepts of a parabola?

If a > 0 (positive) then the parabola opens upward. If a < 0 (negative) then the parabola opens downward. Find the x-intercepts: Notice that the x-intercepts of any graph are points on the x-axis and therefore have y-coordinate 0. We can find these points by plugging 0 in for yand solving the resulting quadratic equation (0 = ax2+ bx + c).

How can you tell if the solutions of a parabola are imaginary?

If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the solutions are real, but irrational (radicals) then we need to approximate their valuesand plot them.