For week 8 of precalc 11 class, we started doing a review for our midterm early in the week and began unit 4 of, doing the first 4 lessons.
Lesson 4.1 was on the properties on a quadratic function and a graph. New concepts such as the vertex, which is the lowest or highest possible point on the parabola graph. Vocabulary and elements of the graph were introduced such as:
- The x-intercept(s): the points where the line passes the x-axis
- The y-intercept(s): the point where the line passes the y-axis
- Vertex: lowest/highest possible point
- Congruent graphs: if the graph has the same shape as the parent function (y = X2)
- Axis of symmetry: the point that splits the graph down vertically
- Direction of opening: whether the graph opens down or up
Aswell the concept that using a table of values, when looking at the output (y) values, if the difference of the difference is the same for each value, the function is quadratic.
Lesson 4.2 and 4.3 were all about solving quadratic equations and transforming them on a graph.
Solving quadratics by inputting them on the graph involved using the parabola shapes, taking the coefficient of the quadratic and turning using that to multiply the input (x), and in lesson 4.3 we learned how to take all the properties of the graph and transform the parent function using them.
Lesson 4.4 was on quadratics using the standard form y = a(x – p)2 + q
in which a represented the stretch or compression,
p is the horizontal translation by the opposite sign I.E. p = –4 means +4 on the x axis
and q represents the vertical translation by the same sign.
Additionally, we learned a conversion on how to change general form (y = ax2+ bx + c) to standard by using completing the square.
y = x2+ 8x + 2
y = x2+ 8x + 16 – 16 + 2
y = (x2+ 8x + 16) – 16 + 2
y = (x + 4)2 – 14