#Quadratic function graph how to#

Step - 3: Find the corresponding values of y by substituting each x value in the given quadratic function.Step - 2: Compute a quadratic function table with two columns x and y with 5 rows (we can take more rows as well) with vertex to be one of the points and take two random values on either side of it.Here are the steps for graphing a quadratic function. i.e., it opens up or down in the U-shape. The graph of a quadratic function is a parabola. y ≤ k (or) (-∞, k] when a y ≥ k (or) [k, ∞) when a > 0 (as the parabola opens up when a > 0).The range of any quadratic function with vertex (h, k) and the equation f(x) = a(x - h) 2 + k is: So, look for the lowermost and uppermost f(x) values on the graph of the function to determine the range of the quadratic function. The range of the quadratic function depends on the graph's opening side and vertex. In interval notation, the domain of any quadratic function is (-∞, ∞). So, the domain of a quadratic function is the set of real numbers, that is, R. Domain of Quadratic FunctionĪ quadratic function is a polynomial function that is defined for all real values of x. The domain of a quadratic function is the set of all x-values that makes the function defined and the range of a quadratic function is the set of all y-values that the function results in by substituting different x-values.

Step - 3: Substitute the values into the intercept form: f(x) = 1 (x - 3)(x - 2).Step - 2: Solve the quadratic equation: x 2 - 5x + 6 = 0.Step - 1: By comparing the given function with f(x) = ax 2 + bx + c, we get a = 1.Step - 4: Substitute the values into the vertex form: f(x) = 2 (x - 2) 2 - 5.Ĭonverting Standard Form of Quadratic Function Into Intercept FormĪ quadratic function f(x) = ax 2 + bx + c can be easily converted into the vertex form f(x) = a (x - p)(x - q) by using the values of p and q (x-intercepts) by solving the quadratic equation ax 2 + bx + c = 0.Įxample: Convert the quadratic function f(x) = x 2 - 5x + 6 into the intercept form.Step - 1: By comparing the given function with f(x) = ax 2 + bx + c, we get a = 2, b = -8, and c = 3.Here is an example.Įxample: Convert the quadratic function f(x) = 2x 2 - 8x + 3 into the vertex form. Converting Standard Form of Quadratic Function Into Vertex FormĪ quadratic function f(x) = ax 2 + bx + c can be easily converted into the vertex form f(x) = a (x - h) 2 + k by using the values h = -b/2a and k = f(-b/2a).

#Quadratic function graph how to#

Let us see how to convert the standard form into each vertex form and intercept form. We can easily convert vertex form or intercept form into standard form by just simplifying the algebraic expressions. We can always convert one form to the other form.

If a < 0, then the parabola opens downward.

If a > 0, then the parabola opens upward.

The parabola opens upwards or downwards as per the value of 'a' varies:

Intercept form: f(x) = a(x - p)(x - q), where a ≠ 0 and (p, 0) and (q, 0) are the x-intercepts of the parabola representing the quadratic function.

Vertex form: f(x) = a(x - h) 2 + k, where a ≠ 0 and (h, k) is the vertex of the parabola representing the quadratic function.

Standard form: f(x) = ax 2 + bx + c, where a ≠ 0.

Here are the general forms of each of them: 1.Ī quadratic function can be in different forms: standard form, vertex form, and intercept form. We will also solve examples based on the concept for a better understanding. You will get to learn about the graphs of quadratic functions, quadratic functions formulas, and other interesting facts about the topic. In this article, we will explore the world of quadratic functions in math. Did you know that when a rocket is launched, its path is described by quadratic function? In other words, a quadratic function is a “polynomial function of degree 2.” There are many scenarios where quadratic functions are used. The word 'Quadratic' is derived from the word 'Quad' which means square. Depending on the coefficient of the highest degree, the direction of the curve is decided. Graphically, they are represented by a parabola.

Quadratic functions are used in different fields of engineering and science to obtain values of different parameters.