In this example, since the parabola opens upward, f(-1.25) = 0.875 is the minimum value of the function. Vertex of a quadratic function is a point where the parabola changes direction and crosses the axis of symmetry. If the parabola opens downward, your answer is the maximum value. If the parabola opens upward, your answer will be the minimum value. To find how many factories should be used to minimize the cost, we need to find the x-coordinate of the vertex. Since x 1, the restaurant will need 1,000 customers. 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. In the function f(x) = 2x^2 + 5x + 4, b = 5 and a = 2. 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. To convert a quadratic from y ax2 + bx + c form to vertex form, y a(x - h)2+ k, you use the process of completing the square. The vertex of a parabola is a point at which the parabola makes its sharpest turn. And the vertex can be found by using the. If it’s negative, the parabola opens downward. In order to find the vertex of the quadratic equation which is represented as ax2+bx+cy which is the standard form. If it’s positive, the parabola opens upward. Find h h, the x x -coordinate of the vertex, by.
Now figure out which direction the parabola opens by checking if a, or the coefficient of x^2, is positive or negative. Given a quadratic function in general form, find the vertex of the parabola. 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.
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