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Missouri EOC Mathematics Flashcards

Missouri EOC Mathematics Flashcards

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Questions and Answers

What is the standard form of a linear equation?

Ax + By = C

What is the slope-intercept form of a linear equation?

y = mx + b

What is the point-slope form of a linear equation?

y - y1 = m(x - x1)

Which of the following is an example of a linear function?

<p>All of the above (D)</p> Signup and view all the answers

What is the vertex quadratic form?

<p>y = a(x - h)^2 + k</p> Signup and view all the answers

What is a quadratic function?

<p>y = ax^2 + bx + c</p> Signup and view all the answers

Which of the following represents a quadratic equation?

<p>Both A and B (D)</p> Signup and view all the answers

What is the general form of an exponential function?

<p>y = ab^x</p> Signup and view all the answers

What is the formula for calculating the slope?

<p>m = (y2 - y1) / (x2 - x1)</p> Signup and view all the answers

What is the formula for the nth term of an arithmetic sequence?

<p>An = a1 + (n - 1)d</p> Signup and view all the answers

What is the distance formula?

<p>D = √((x2 - x1)^2 + (y2 - y1)^2)</p> Signup and view all the answers

What is the midpoint formula?

<p>(x1 + x2)/2, (y1 + y2)/2</p> Signup and view all the answers

What is the quadratic formula?

<p>x = -b ± √(b^2 - 4ac) / (2a)</p> Signup and view all the answers

What theorem relates the sides of a right triangle?

<p>a^2 + b^2 = c^2</p> Signup and view all the answers

What is the formula for distance in relation to rate and time?

<p>d = rt</p> Signup and view all the answers

What is the representation of a linear function shown in an example?

<p>y = 3x + 1</p> Signup and view all the answers

What does an absolute value function look like?

<p>y = |x| - 2</p> Signup and view all the answers

What is the form of an exponential function given by 2 and 3?

<p>y = 2 * 3^x</p> Signup and view all the answers

What is an example of a quadratic function?

<p>y = 3x^2</p> Signup and view all the answers

Flashcards

Standard form of a linear equation?

Ax + By = C, where A, B, and C are constants.

Slope-intercept form?

y = mx + b, where m is the slope and b is the y-intercept.

Point-slope form?

y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Vertex form?

y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

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Quadratic function?

y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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General form of an exponential function?

y = ab^x, where a is the initial value and b is the base.

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Formula for slope?

m = (y2 - y1) / (x2 - x1)

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nth term of an arithmetic sequence?

An = a1 + (n - 1)d, where a1 is the first term, n is the term number, and d is the common difference.

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Distance formula?

D = √((x2 - x1)^2 + (y2 - y1)^2)

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Midpoint formula?

((x1 + x2)/2, (y1 + y2)/2)

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Quadratic formula?

x = (-b ± √(b^2 - 4ac)) / (2a)

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Pythagorean theorem?

a^2 + b^2 = c^2, where a and b are legs, and c is the hypotenuse.

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Distance formula?

d = rt, where d is distance, r is rate, and t is time.

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Example of a linear function?

y = 3x + 1 is a line where slope is 3 and y-intercept is 1.

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Absolute value function?

y = |x| - 2 is a V-shaped graph, shifted down 2 units.

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Exponential function example?

y = 2 * 3^x is an exponential growth function with initial value 2.

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An example of a quadratic function?

y = 3x^2 represents a parabola.

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Study Notes

Linear Functions

Standard form: Ax + By = C
Slope-intercept form: y = mx + b
Point-slope form: y - y1 = m(x - x1)

Quadratic Functions

Vertex form: y = a(x - h)^2 + k
Standard quadratic form: y = ax^2 + bx + c
Quadratics encompass both vertex form and standard form.

Exponential Functions

General form: y = ab^x
Example: y = 2 * 3^x illustrates exponential growth.

Arithmetic Sequence

Formula: An = a1 + (n - 1)d
Used to find the n-th term in an arithmetic sequence.

Distance and Midpoint

Distance formula: D = √((x2 - x1)^2 + (y2 - y1)^2)
Midpoint formula: (x1 + x2)/2, (y1 + y2)/2

Essential Theorems

Quadratic formula: x = -b ± √(b^2 - 4ac) / 2a for finding roots of a quadratic equation.
Pythagorean Theorem: a^2 + b^2 = c^2, relates sides of a right triangle.

Rate, Time, and Distance

Distance formula: d = rt, where distance equals rate multiplied by time.

Various Function Forms

Example linear function: y = 3x + 1
Example absolute value function: y = |x| - 2
Example quadratic function: y = 3x^2

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