HPC Calc, Circle, Exp Notes

HPC Calc, Circle, Exp Rev. Notes

Review exponent rules, calculator, and circle distance

How to use calculator

• Zeros) Left bound is LHS of the zero, right bound is RHS of the zero. Move the cursor accordingly hit ENTER to verify.

• When a is +, vertex is a minimum.

• When a is +, vertex is a minimum.

Multiple Choice

Find the maximum of the given function to the nearest hundredth.

 $y=-1.8x^2+8x-6$  
Hint: maximum or minimum is the y-value of the vertex. 
2nd Calc Max Left bound enter Right bound enter Guess ENTER

• 2.22

• 2.89

• 8.29

• 4

Equation of a circle

• (x - h)²+(y - k)² = r²

• (h, k) is the center of the circle, r is the radius.

• (x - 5)²+(y + 3)² = 25; Center (5, -3), r = 5

Multiple Choice

What are the coordinates of the center and the radius of the circle with an equation:

(x + 7)² + (y - 6)² = 64 ?

• Center (7,-6)

  Radius = 8 units

• Center (-7,6)

  Radius = 64 units

• Center (-7,6)

  Radius = 8 units

• Center (7,-6)

  Radius = 64 units

Distance formula & midpoint

•  $d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$  

•  $Midpoint\ =\ \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$  

Multiple Choice

Find the distance between the two points: (2, -1) and (2, 5)

• 0
• 8.3
• 6
• 5.5

Multiple Choice

Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)

• (-1, 13)
• (13, 1)
• (13, -1)
• (5, 13)

Rules for exponents

•  $x^{12}\cdot x^7=x^{19}$  

•  $\frac{x^{15}}{x^9}=x^{15-9}=x^6$  

•  $\left(x^4\right)^7=x^{28}$  

•  $\left(2xy^2z^3\right)^2=4x^2y^4z^6$  

•  $\left(\frac{2}{x}\right)^3=\frac{8}{x^3}$  

•  $x^0=1,\ x\ne0$  

•  $x^{-2}=\frac{1}{x^2},\ x\ne0$  ;  $x^{\frac{3}{4}}=^4\sqrt{x^3}$  

Multiple Choice

Simplify

• A

• B

• C

• D

Multiple Choice

Rewrite using a positive exponent.

g^-7

• ¹/_g⁷

• g⁷

• ¹/_g^-7

• -g⁷

Multiple Choice

Simplify

• x⁴

• x⁶

• x²⁹

• x²⁰

Multiple Choice

How would you write 0.0005 in scientific notation?

• 50 x 10^-5

• 5 x 10^-4

• 5 x 10^-3

• .5 x 10³

Multiple Choice

The rule of scientific notation is to write all exponents with a base of ____.

• 50

• 5

• 100

• 10