Both the coordinates of the vertex are given as (+2  -9). The value of the y coordinate (-3) of the vertex is the minimum value of the quadratic function. Set up the function in it’s standard or vertex form by completing the square method. Finding the Maximum or Minimum. And I think it’s something that almost all of... We've created a Free Algebra Mastery Course below. Whenever parabola open upwards, we find the minimum value of the quadratic function. For example, if you’re starting with the function f(x) = 3x + 2x - x^2 + 3x^2 + 4, you would combine the x^2 and x terms to simplify and end up with f(x) = 2x^2 + 5x + 4. Because he was finding the minimum value. Replacing with +1 in the function to calculate the y coordinate of the vertex we get: The above evaluation shows that the y coordinate of the vertex is 6. 20 May 2020. quadratic; 2) Find the vertical intercept; 3) Find the horizontal intercept(s), i.e. By using our site, you agree to our. The general form is f(x)=ax2+bx+c{\displaystyle f(x)=ax^{2}+bx+c}. First shift the last term of the function to the left side and form an equation as: Now half the co-efficient of x term and add it’s square to both sides of the equation. I believe if we master over few formulas and some basic algebra rules, quadratic functions would become even easier. To find the maximum or minimum value of a quadratic function, start with the general form of the function and combine any similar terms. As a second example, consider the function, If your function is already given to you in this form, you just need to recognize the variables, To review how to complete the square, see. To find the maximum or minimum value of quadratic functions, you need to: To have a clear understanding of this topic, it’s important to address every basic detail of quadratic function. It is what makes us look and search for ways by which we can improve our algebra skills, right? Find the value of equal to . At x = 0, the function has value 0, so this must be the minimum. Find the co-responding value of the y coordinate of the vertex by putting the value of x coordinate in the original function. This tutorial shows you how! Jake Adams. Since it is opening upwards, we have to find the minimum value of the quadratic function. In case of a positive value, the graph would be a parabola opening upwards. This is the x coordinate of the vertex. It is a ‘U’ shaped curve that either opens upward or downward depending upon the co-efficient of the term. Next, find the x value of the vertex by solving -b/2a, where b is the coefficient in front of x and a is the coefficient in front of x^2. The y-coordinate of the vertex is – 9. Therefore, we find the maximum value of the quadratic function. The graph of function f(x)=-x²-4x-5 is given as: The graph of the above function shows a parabola opening downwards. While determining the x-coordinate, the sign of h variable in the parenthesis is reversed. 1. The above function is present in its general form. Beginning with the General Form of the Function, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2a\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1-Version-4.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1-Version-4.jpg","bigUrl":"\/images\/thumb\/2\/2a\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1-Version-4.jpg\/aid2443845-v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"