unit 4 quiz 3 sat math khan academy

height vs. time

standard form: h(t) = -at2 + bt + c

h(t) is the height

t is the time

c is the initial height of the object (y-intercept)

the maximum height of the object is b/2a (x-value of the vertex)

population growth and decline

P(t) = P₀r^t

P₀ is the initial population (y-intercept)

the population is multipled by r (%) each year

t = time

compounding interest

P(t) = P₀(1+r)^t

P₀ = initial amount of money (y-intercept)

r = interest rate applied each year (interest rate is r%)

t = time

vertex

maximum/minimum y-value of the parabola

x-intercept

can also be called zero and root

always plug in 0 for x, don’t just cancel out terms with x in them

root

can also be called zero and x-intercept

zero

can also be called root and x-intercept

how many x-intercepts does a parabola have

2 if the discriminant is positive

1 if the dis. is zero (the vertex is on the x-axis)

0 if the dis. is negative

what are the types of quadratic equations

1. height vs. time

2. population growth and decline

3. compounding interest

how do you find the zeros of f(x) = x²+7x+12

1. zero means x-intercept

2. x-intercept is when y = 0

3. to find x, factor it (x + 3)(x + 4)

4. the zeros are -3 and -4

if y = f(-x),

then it’s reflected across the x-axis

if y = -f(x),

then it’s reflected across the y-axis

y and x-intercepts

is always when x = 0

take y = 2^x + 1 for example

the y-intercept is not 1. always plug in 0 for x:

y = 2⁽⁰⁾ + 1

y = 1 + 1

horizontal asymptote

horizontal line that the graph approaches but never reaches (as the x-value decreases, the y-value approaches _)

exponential graph

y = ab^x + c

c is the horizontal asymptote

y-intercept is 1 + c

how to find vertical asymptote

set the denominator = to zero, solve for x

y = axⁿ

if a > 0, then y approaches positive ∞

if a < 0, then y approaches negative ∞

if n is even, then the ends of the graph point in the same direction

if n is odd, then the ends of the graph point in different directions