# 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.

# Week 8 – Precalc 11

For the eighth week of Precalc 11, we started our new unit — Analyzing Quadratic Functions and inequalities.

Key Learning：

Every quadratic function can be written in the form y = ax^2+bx+c, where a, b, and c are real numbers and a is not zero.

First, we learned the properties of quadratic functions and how to analyze the quadratic equation. We learned that when are given the quadratic equation in vertex form then we can graph the equation.

Second, we learned the quadratic equation $ax^2 + bx + c = 0$, this unit we learned $y = a(x-p)^2 + q$. This is combination of the equations $y = (x-p)^2, y = x^2$, and $y = x^2 + q$. These equations are all very important in graphing the curve the equations make.

Example：

Graph y = (x− 2)^2− 4

• Vertex = (2,4)
• x-intercept: 0 and 4
• y-intercept: 0
• opens up (happy)

# Dimensional Motion—Design Lab

#### Dimensional Motion—Design Lab

Purpose: To determine the muzzle velocity(vi) of a Nerf.

Materials:

• Stopwatch
• Nerf Gun
• Slope finder App to make sure it is 90 degrees straight up.

Procedure:

1. Fire Nerf Gun vertically, at 90 degrees, use the slope finder App to make sure it is 90 degrees straight up. Determine the time when a bullet is fired and when it lands (total time).
2. Divide time by 2 to find the time of when the bullet gets to the peak height.

Total Time/2 = Time gets to the peak height.

1. Record the data below.
2. Use the Kinematic equation to calculate the initial velocity.

Formula: Vf=Vo+at

1. Find percent difference (keep 3 sig figs) between your groups vs. other groups.

% difference= |your group data – other groups data| x 100%
Average data

Data: Nerf Gun chart

 Total time(s) Time for going upward(s) Vf(m/s) Vo=? (m/s) [upward] 1 4.20 2.11 0 20.7 2 4.13 2.07 0 20.3 3 4.36 2.18 0 21.4 4 4.05 2.03 0 19.9 5 3.80 1.90 0 18.6 Average 4.11 2.06 0 20.2

Calculations:

Show all work clearly.

% difference:

% difference= |your group data – other groups data| x 100%
Average data

Conclusion:

In this lab, we studied the muzzle velocity of a Nerf Gun. Because the bullet reaches the highest point and then landed at half the time the bullets reached the highest point, our time will be divided by the total time recorded. (Total Time/2 = Time gets to the peak height.) Then use the calculation formula (Vf = Vo + at) to get the initial velocity. Combining these two equations, we get the result of our initial velocity of a nerf gun is 20.2m/s

Errors in this lab came from our measurement. No measurement can be perfect. Measurements always have some uncertainty. Due to the presence of measurement uncertainty, measured values will never be equal to predicted values. This causes our error value with other groups to be around 8-18%. If we experiment on a sunny day instead of a rainy day, the results will improve, as this will not use images for the weight of the bullet. Second, the wind has a large impact on the data, which will affect the direction of the bullet, which may increase the time the bullet stays in the air. If done correctly, this will reduce our error in calculating time.

Designed by: Lina, Bianca, Grace

Oct. 15, 2019

# Week 4 – Precalc 11

For the fourth week of Precalc 11, we continued studying about “Radical Operation and Equations” unit.

First, we learned how to Multiply & Divide Radicals.

When we are multiplying radicals (with the same index), we need to multiply under the radical first, and then multiply in front of the radical (any values multiplied times the radicals).

When we are dividing radicals (with the same index),  we need to divide under the radical first, and then divide in front of the radical (divide any values multiplied times the radicals).

And also to divide radical expressions with the same index, we use the quotient rule for radicals. If a and b represent nonnegative numbers, where ,  then we have:

# Week 3 – Precalc 11

For the third week of Precalc 11, we started our new unit “Radical Operation and Equations”.

We learned how to write an entire radical to a mixed radical and how to write a mixed radical to an entire radical.

And we also learned how to add or subtract radicals. Like terms are radicals with the same index and radicand, these are the only radicals that can be + or- . When there is a variable in the radicand, you must specify what type of number (positive or negative) is needed to make the radical defined, for √ , the radicand must be a positive number.

# Week 2 – Precalc 11

For the second week of Precalc 11, we continued studying about “Roots and Powers”.

We learned power with positive rational exponent and negative rational exponent.

We also learned Exponent Laws and Order of Operations which is applying the order of operations and exponent laws to evaluate numerical expressions and simplify algebraic expressions. We can recall “BADMAS” for remembering the order：

B (brackets)  E (exponents)  D/M (divided or multiply )  A/S (add or subtract)

And through the skill check 2, I noticed an exponent law that is very easy to make mistakes, that is !!! $a^0$ = 1 !!!

# Week 1 – Precalc 11

For the first week of Precalc 11, we did a little bit review of Math 10 staff and started our new unit “Roots and Powers”.

First, in the review part, I learned a new method to factor the polynomials. Which is called “Box Method” , to me it is a more clearly and visualized way to shows the factoring process.

I made a mistake at the beginning with this following polynomial but after Ms. Burton taught us the “box method” , it makes more sense to me.

In the new unit, I learned how to evaluate the fraction radical.