Tom is sketching the graph of a quadratic function. He is asking his friends about how many x-intercepts his function can have. Here is the feedback from his friend.
Allison says the graph can have 1 x-intercept.
Carson says the graph can have no x-intercepts.
Dolly says the graph must have two x-intercepts.
Erica says the graph can have, at most, 1 x-intercept.
How many of Tom's friends are right and why?
A
0
B) 1: Dolly is right because a quadratic graph has exactly two x-intercepts.
C 2: Allison and Carson are right because the graph can have 0 or 1 x-intercepts.
D 3: Allison, Carson, and Erica are right because the graph can have 0, 1, or 2 x-intercepts.
E4; They are all right because the graph can have a varying number of x-intercepts.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)