Match each graph with its function. Please help

graph 1: f(x) = 3*x^2 - 5*x

graph 2: f(x) = 3*x^2 + 5

graph 3: f(x) = -3*x^2 - 5

Step-by-step explanation:

This is ratter easy if we know some of the main rules for quadratic equations.

For a quadratic equation:

y = f(x) = a*x^2 + b*x + c

if a > 0, then the arms of the graph will open upwards.

if a < 0, then the arms of the graph open downwards.

With this in mind we can look at the graphs, only one of them have arms that open downwards, then the function that matches with this graph should be the only one with a leading coefficient smaller than zero, which is:

f(x) = -3*x^2 - 5

Now, when we have functions like:

y = f(x) = a*x^2 + c

c is the value of y at the vertex.

In graph 2 we can see that the arms open upwards, and that the y-value at the vertex is positive (it is above the horizontal axis)

Then the function of graph 2 should have a positive leading coefficient and a positive constant term.

The function is:

f(x) = 3*x^2 + 5

Then the remaining function is the one that corresponds to graph 1

f(x) = 3*x^2 - 5*x

Then we have:

graph 1: f(x) = 3*x^2 - 5*x

graph 2: f(x) = 3*x^2 + 5

graph 3: f(x) = -3*x^2 - 5

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560