Question

1. move cursor near intercept, choose left bound, right bound, enter. practice: for y = x² + 2x - 8, find both zeros. part 3: tables (10 minutes) a. making a table 1. enter y = x² - 4x + 3. 2. press 2nd → graph (table). practice: fill in values: x: -2, 0, 1, 5 y: b. changing table settings 1. press 2nd → window (tblset). 2. set tblstart = -5, δtbl = 0.5. 3. check 2nd → graph. practice: whats different? part 4: statistics (15 minutes) a. entering data 1. press stat → 1: edit. 2. enter 85, 90, 76, 100, 92 into l1. b. finding mean & median 1. stat → calc → 1: 1 - var stats → l1 (2nd → 1). 2. enter. mean = median = practice: enter 5 favorite numbers into l2. mean = median = part 5: applications (15 minutes) option a - car loan 1. apps → finance → 1: tvm solver. 2. n = 60, i% = 6, pv = -10000, fv = 0, p/y = 12. 3. solve for pmt. monthly payment = option b - regression 1. l1 = 1,2,3,4,5, l2 = 2,4,6,8,10. 2. stat → calc → 4: linreg(ax + b). equation y = option c - geometry circle

Explanation:

Step1: Find zeros of quadratic

Set $y = 0$ and factor.

Step2: Evaluate function

Substitute $x$ values into $y=x^{2}-4x + 3$.

Step3: Calculate mean

Sum data and divide by count.

Step4: Find median

Order data and pick middle value.

Step5: Solve TVM for PMT

Use TVM formula and substitute values.

Step6: Find regression equation

Use calculator's regression function.

Answer:

For the quadratic - function $y=x^{2}+2x - 8$:

The zeros are found by setting $y = 0$. So, $x^{2}+2x - 8=0$. Factoring gives $(x + 4)(x - 2)=0$. Then $x=-4$ and $x = 2$.

For the function $y=x^{2}-4x + 3$:

When $x=-2$, $y=(-2)^{2}-4\times(-2)+3=4 + 8+3 = 15$.
When $x = 0$, $y=0^{2}-4\times0+3=3$.
When $x = 1$, $y=1^{2}-4\times1+3=1 - 4+3=0$.
When $x = 5$, $y=5^{2}-4\times5+3=25 - 20+3=8$.

For the statistics part with data [85, 90, 76, 100, 92] in L1:

The mean $\bar{x}=\frac{85 + 90+76+100+92}{5}=\frac{443}{5}=88.6$. The median is the middle - value when the data is ordered. Ordered data: [76, 85, 90, 92, 100], so the median is 90.

For the car - loan problem (Option A):

We use the TVM (Time - Value of Money) formula. The TVM formula for the present value of an ordinary annuity is $PV=PMT\times\frac{1-(1 + \frac{I}{100P/Y})^{-N\times P/Y}}{\frac{I}{100P/Y}}$.
Here, $N = 60$ (number of periods), $I\%=6$ (annual interest rate), $PV=- 10000$ (present value, negative because it's the amount received), $FV = 0$ (future value), $P/Y = 12$ (payments per year).
First, $r=\frac{6}{100\times12}=0.005$.
$10000=PMT\times\frac{1-(1 + 0.005)^{-60}}{0.005}$.
Let $a=(1 + 0.005)^{-60}\approx0.741372$.
$1-(1 + 0.005)^{-60}=1 - 0.741372 = 0.258628$.
$\frac{1-(1 + 0.005)^{-60}}{0.005}=\frac{0.258628}{0.005}=51.7256$.
$PMT=\frac{10000}{51.7256}\approx193.32$.

For the regression problem (Option B):

Using a calculator for linear regression with $L1=[1,2,3,4,5]$ and $L2=[2,4,6,8,10]$.
The linear regression equation $y = ax + b$.
The calculator will give $a = 2$ and $b = 0$, so the equation is $y = 2x$.