Week 9 – Precalc 11

For the ninth week of Precalc 11, we learned more about the Analyzing Quadratic Functions and inequalities unit.

Key Learning:

  1. Vertex Form a(x-p)^2 + q = y
  2. General Form ax^2 + bx +c = y
  3. Factored Form a(x-x_1)(x-x_2) = y

We learned equivalent forms in order to solve equations by using 3 different formulas.

 vertex form- y = a (x-p)^2 + q, where (p, q) is the vertex of the parabola, and a is the stretch value. It’s the easiest equation to graph because we are given a starting point and the pattern that it goes up by.

general form- y = ax^2 + bx + c,  a, b, and c are three real numbers. Once these are given, the values for x and y that make the statement true express a set of (x, y) points which form a parabola when graphed. It’s the most useless equation to graph because we are only given the y-intercept and can’t do much else unless it’s converted to one of the other forms.

factored form– y = a(x-x1)(x-x2),  x1 and x2 are the opposite of the x-intercepts of a graph. This equation is useful only when given the x-intercepts and is used mostly when trying to search for a value as long as there is another point given along the parabola to substitute y and x for to find a.

 

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