How do I read the equation (function) y=-0.03x^2+0.14x+1.43?
Do I have to complete the square to find the vertex, max., min., etc.? This function is part of a word problem that I am trying to do. I would appreciate any help.
Well, you could multiply everything by 100 to get an easier function:
y=-3x^2+14x+143
in which you could try and use the quadratic theorem
[-b +/- sqrt(b^2-4ac)]/2a
Giving you:
-14 +/- sqrt(196-(-1716)/-60
[-14 +/- sqrt(1912) ]/-6
You cant simplify too much. But you get the idea from here. Is this the answer you were looking for?
To read the equation y = -0.03x^2 + 0.14x + 1.43, you can break it down as follows:
1. The equation is in the form of a quadratic function: y = ax^2 + bx + c, where a, b, and c are coefficients.
2. In this case, a = -0.03, b = 0.14, and c = 1.43.
Now, let's address your question about finding the vertex, maximum/minimum, and other details of the function. Yes, you can complete the square to find these parameters.
To find the vertex:
1. First, rewrite the equation in the vertex form by completing the square: y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
2. Rearrange the equation to isolate the x^2 and x terms: y = -0.03(x^2 - (4.67)x) + 1.43.
3. Complete the square inside the parentheses: y = -0.03(x^2 - (4.67)x + (4.67/2)^2) + 1.43 + 0.03(4.67/2)^2.
4. Simplify and rewrite: y = -0.03(x - 2.33)^2 + 2.85.
From this form, you can identify the vertex as (2.33, 2.85). The x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of x^2 and x, respectively.
Regarding the maximum or minimum, you can determine it based on the coefficient of the x^2 term (a).
- If a > 0, the parabola opens upwards, and the vertex represents the minimum point.
- If a < 0, the parabola opens downwards, and the vertex represents the maximum point.
In this case, since a = -0.03 < 0, the parabola opens downwards, and the vertex (2.33, 2.85) represents the maximum point.
I hope this explanation helps you understand how to read the equation and find the vertex, maximum/minimum for your word problem. Let me know if you have any further questions!