Podcast
Questions and Answers
What is the length of the radius of the circle in the equation $(x - 7)^2 + (y - 8)^2 = 100$?
What is the length of the radius of the circle in the equation $(x - 7)^2 + (y - 8)^2 = 100$?
- 10 (correct)
- 20
- 12
- 5
What is the first step in graphing a circle written in general form?
What is the first step in graphing a circle written in general form?
- Determine the radius
- Rewrite the equation in center-radius form (correct)
- Plot the center point
- Identify the center coordinates
Will Jerry receive a signal from the tower located at (3, 5) if his house is at (3, -8)?
Will Jerry receive a signal from the tower located at (3, 5) if his house is at (3, -8)?
- Yes, but only at certain times
- Yes, within the signal radius
- No, because the tower's signal is weak
- No, because his house is outside the signal reach (correct)
What can be said about the distances among points Q, R, and S, given that R is the midpoint of QS?
What can be said about the distances among points Q, R, and S, given that R is the midpoint of QS?
What type of arc is formed if the measure of arc AB is 100 degrees?
What type of arc is formed if the measure of arc AB is 100 degrees?
To determine the measure of an angle inscribed in a circle, what is the first step?
To determine the measure of an angle inscribed in a circle, what is the first step?
What should be noted about the maximum number of turning points of a polynomial graph?
What should be noted about the maximum number of turning points of a polynomial graph?
Which condition is NOT part of determining whether a function is a polynomial?
Which condition is NOT part of determining whether a function is a polynomial?
What is the leading coefficient of the polynomial function f(x) = 4x + 2x^3 + 1?
What is the leading coefficient of the polynomial function f(x) = 4x + 2x^3 + 1?
What type of polynomial function is defined as a first-degree polynomial?
What type of polynomial function is defined as a first-degree polynomial?
Which of the following is an example of a polynomial function in standard form?
Which of the following is an example of a polynomial function in standard form?
What is the formula for the midpoint of a segment given points (x1, y1) and (x2, y2)?
What is the formula for the midpoint of a segment given points (x1, y1) and (x2, y2)?
Which equation describes a circle with center at point (h, k) and radius r?
Which equation describes a circle with center at point (h, k) and radius r?
What represents the height (H) of a rectangular box whose volume (V) is 6000 cm³, length (L) is 30 cm, and width (W) is 20 cm?
What represents the height (H) of a rectangular box whose volume (V) is 6000 cm³, length (L) is 30 cm, and width (W) is 20 cm?
What type of angle is ∠GOL if it is inscribed in a circle and intercepts the diameter GL?
What type of angle is ∠GOL if it is inscribed in a circle and intercepts the diameter GL?
What are the x-intercepts of the polynomial function y = (x + 4)(x + 2)(x - 1)(x - 3)?
What are the x-intercepts of the polynomial function y = (x + 4)(x + 2)(x - 1)(x - 3)?
Flashcards
Leading Coefficient Test
Leading Coefficient Test
A test that uses the leading term of a polynomial function to determine how the graph behaves on the right and left ends.
Linear Function
Linear Function
A polynomial function of the first degree.
Polynomial Function (Standard Form)
Polynomial Function (Standard Form)
A polynomial function written with terms ordered in descending powers of the variable.
Midpoint Formula
Midpoint Formula
Signup and view all the flashcards
Equation of a Circle
Equation of a Circle
Signup and view all the flashcards
Circle Equation
Circle Equation
Signup and view all the flashcards
X-intercepts (Factored Form)
X-intercepts (Factored Form)
Signup and view all the flashcards
Tangent to a Circle
Tangent to a Circle
Signup and view all the flashcards
Circle radius equation
Circle radius equation
Signup and view all the flashcards
Graphing a circle equation
Graphing a circle equation
Signup and view all the flashcards
Signal reach of a tower
Signal reach of a tower
Signup and view all the flashcards
Midpoint distance
Midpoint distance
Signup and view all the flashcards
Minor arc
Minor arc
Signup and view all the flashcards
Finding angle measure
Finding angle measure
Signup and view all the flashcards
Center of a circle
Center of a circle
Signup and view all the flashcards
Study Notes
Polynomial Functions
- Leading Coefficient Test determines the right & left-hand behavior of a polynomial function's graph; leading coefficient of f(x) = 4x + 2x³ + 1 is 2
- A polynomial function of degree 1 is a linear function
- Example of a polynomial function in standard form: f(x) = 5x³ + x² + 6x + 8
- Midpoint coordinates: ((x₁ + x₂)/2, (y₁ + y₂)/2)
Circles
- Equation of a circle with center (h, k) and radius r: (x - h)² + (y - k)² = r²
- Volume of a rectangular box: V = LWH
- Given volume 6000 cm³, length 30 cm, width 20 cm; height is 6000 / (30 * 20) = 10 cm.
- A semi-circle is an arc that spans half the circle.
- Inscribed angle: an angle formed by two chords that share a common endpoint on a circle; for ∠GOL, if m∠GOL = 1/2, then ∠GOL is inscribed.
- To graph polynomial functions, find x-intercepts; for y = (x + 4)(x + 2)(x - 1)(x - 3), x-intercepts are -4, -2, 1, and 3.
- A tangent line intersects a circle at exactly one point.
- Plotting points accurately is the first step for determining the figure they form.
- Distance between two points (x₁, y₁) and (x₂, y₂): √((x₂ - x₁)² + (y₂ - y₁)²).
- Equation (x - 7)² + (y - 8)² = 100; radius is 10
- First step in graphing a circle from general form (x² + y² + Dx + Ey + F = 0) is to rewrite it in center-radius form.
Geometry
-
Types of arcs: minor arc (less than 180°), major arc (greater than 180°)
-
Intercepted arc: an arc whose endpoints are on the sides of an inscribed angle. If m∠ABD is needed, first find the measure of its intercepted arc AE.
-
Cubic polynomial functions are relevant to calculating volumes of boxes.
-
Finding the measure of an inscribed angle involves multiplying the measure of its intercepted arc by ½. Polynomial transformation involves converting a polynomial function to standard form.
-
Polynomial functions can have a maximum of n - 1 turning points where n is the degree of the polynomial (This statement isn't always true because a function can have fewer than n-1, e.g., a parabola is a quadratic which means n is 2 and the max turning point may be just 1).
-
A condition for a function to be a polynomial is that the exponents of variables should not be in the denominator.
-
A circle can be divided into six congruent arcs by six points on the circumference; each arc measures 60 degrees.
-
A segment of a circle is part of a circle.
-
The measure of an angle formed by two radii is the same as the measure of the arc between those two radii. (e.g., m∠ LOE = m arc LE).
Graphs
- Graph end behavior is described as rising to the left & right
- A chord is a line segment whose endpoints both lie on a circle.
- A sector of a circle is a region bounded by two radii and an arc.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
