A quadratic has four main parts: the vertex (max/min), x-intercepts, y-intercepts, and an axis of symmetry. Each part plays a key role in the creating and understanding of a parabolic graph. By taking an equation in standard form and manipulating it into a more easily graphed parent function, problem solvers are able to retrieve important information.
The problem solver does have to pay attention to the details in order to be sure that their work is correct! For example, it is essential that the parent function follow the correct form: f(x) = a(x-h)^2+k. Once the problem is correctly converted into the parent function form, they can easily withdraw information from it. The vertex (h,k), x-intercepts (y=0), the y-intercept (x=0), and the axis of symmetry (x=h)! With these simple equations, the problem solver is on their way to a great graph! What they must remember is that the work has to be transferred correctly!
Explain
You are given the problem: f(x) = 4x^2+24x-2. The first step is to add a 2 to both sides. Next, you factor out the constant from the leading value out of both the first and second term (don't forget to add it to the other side as well!). To find the missing term, use the formula "b/2^2". You then fill in the answer into the two blanks. Finally you simplify it to make it into the parent graph equation! Lastly, use the given formulas to discover the vertex, y-intercept, x-intercepts, and axis of symmetry.
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