For identifying the minimum or maximum on a graph, look at the images below:
To determine if you have a maximum or a minimum from an equation, you will need to look at the value of the x2.
If POSITIVE, then your graph will be facing upwards and you will have a minimum.
If NEGATIVE, then your graph will be facing downwards and you will have a maximum.
Determine if y = -32 - 5x + 2, will have a maximum or a minimum.
The value with the x2 is -3. Since this value is negative, the graph will be facing downwards and have a maximum.
Recall, that the General Form of a parabola is y = ax2 + bx + c. In order to find the vertex from this form, you must first find the x-coordinate of the vertex which is x = - b/2a. After you find the x-coordinate of the vertex, you will take this number and substitute for x in the parabola equation. You then will be able to find the y-coordinate of the vertex.
Find the vertex of the parabola y = x2 - 6x + 3.
Step 1: Using the general form y = ax2 + bx + c, identify a and b.
a = 1 and b -6
Step 2: Substitute your values into x-coordinate formula and simplify.
Step 3: Substitute x = 3 into the equation y = x2 - 6x + 3 and simplify.
y = x2 - 6x + 3 = (3)2 - 6(3) + 3 = 9 - 18 + 3 = -6
Thus, the vertex of the parabola is (3, -6)
Recall, that the Standard Form of a Parabola is y = a(x-h)2 + k. To find the vertex in this form, you will use identify h and k from the standard form and put it into the vertex point (h, k).
Find the vertex of the parabola y = 2(x-1)2 + 3.
Step 1: Using the Standard Form y = a(x - h)2 + k, identify (h, k)
h = 1 and k = 3
The vertex is (1, 3).