The vertex is also called the . The vertex is the point on the parabola that the function is either at the or value. The of is the vertical line through the that divides the parabola into two halves.

The x-intercept(s) are where the function value is . There may be , or x-intercepts of a parabola.
These points are called or . The expressions (x – r1) and (x-r2), where
r1 and r2 are the x values that produce a function value of zero, are called the of the quadratic.

The y-intercept of a parabola is the point where the x value is . A parabola always has y-intercept.

The domain of any function (including quadratic functions) is the set of all possible x-values. Typically, the domain of a parabola is ___
numbers.
The range of any function (including quadratic functions) is the set of all possible y-values. The range of a quadratic function depends on the and whether the parabola “opens up” or “opens down”. The y values will have either a or a value.

There are forms of quadratic functions:
Standard Form is f(x) = ax2 + bx + c where a cannot equal , but b and c can be any real number. If a 0, then the parabola opens .
The x coordinate of the vertex and axis of symmetry can be found with the expression .
Vertex Form is f(x) = a(x-h)2 +k where a cannot equal , but h and k can be any real number. The point (h, k) is the .
Factored Form is f(x) = a(x-r1)(x-r2) where a cannot equal , but r1 and r1 can be any complex number (including imaginary numbers – more about this later).

In a sample of 2023 u.s. adults, 373 said franklin roosevelt was the best president since world war ii. two u.s. adults are selected at random from the population of all u.s. adults without replacement. assuming the sample is representative of all u.s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.

Type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar. consider the given table.

Analyze the graph of the cube root function shown on the right to determine the transformations of the parent function. then, determine the values of a, h, and k in the general equation. y=a3x-h+k h= . k= done 000000l o 7 of 8