If the parabola opens downward, your answer is the maximum value. If the parabola opens upward, your answer will be the minimum value.

Finally, plug the x value into the function to find the value of f(x), which is the minimum or maximum value of the function. Therefore, you would divide -5 by 2 times 2, or 4, and get -1.25. Quadratics don’t necessarily have all positive terms, either. The variables b or c can be 0, but a cannot. It wouldn’t be a quadratic expression anymore. If a were allowed to be 0, then the x to the power of 2 would be multiplied by zero. In the function f(x) = 2x^2 + 5x + 4, b = 5 and a = 2. In a quadratic expression, the a (the variable raised to the second power) can’t be zero. 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. In the function f(x) = 2x^2 + 5x + 4, the coefficient of x^2 is positive, so the parabola opens upward. Given a quadratic function in standard form: f(x) ax². Each letter in the standard form equation tells us a piece of information about the parabola, just like the letters from the vertex form equation had. An equation written in standard form is yet another equation that forms a parabola when graphed. We don’t need to factor the quadratic equation because factoring is only a special case of finding the 2 real roots. The equation for standard form is written as yax2+bx+c. If it’s negative, the parabola opens downward. We can convert a quadratic function from standard form, y ax² + bx + c, to the general vertex form: y a(x + p)² + q. If it’s positive, the parabola opens upward. Now figure out which direction the parabola opens by checking if a, or the coefficient of x^2, is positive or negative. 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. To find the maximum or minimum value of a quadratic function, start with the general form of the function and combine any similar terms.

Standard form quadratic