1. Solve by Applying the Quadratic Formula Show Your Work

# 1. solve by applying the quadratic formula show your work

x ^2 + 4x + 13=0

There is no real solution as discriminant (the expression under the square root is negative)

#2 Use the discriminant method to determine

5a^2 -6a +1 =0

a) 2 different imaginary solutions

b) 2 different rational solutions

c) 2 different irrational solutions

d) exactly one rational solution

It is a perfect square 4*4=16>0, hence you have 2 different rational solutions.

#3) Use the quadratic formula to determine x- intercepts if any of this function

f (x) = 1/2 x ^2 then graph and I know how to graph.

½*x^2=0  x=0 is the only solution so the intercept is x=0, in fact it is a vertex of your parabola as well.

#4 Without graphing find the vertex. f (x ) =3 (x +sqrt 11^2 -17.31

a) sqrt 11, -17.31

b) ( 3 -17.31 )

c) ( -17.31 - sqrt 11)

d) ( sqrt 11, - 17.31)

#5) Without graphing find the line of symmetry f (x) =7 ( x- 9) ^2 -2 a) x- negative 9 b) x- negative 2 c) x =9 d) y= neg 2 –

Line of symmetry is defined by the vertex – the minimal value of y is given at x=9, hence the symmetry line is x=9

#6. F(X) = -3 ( x+ 7)^2-2 Without graphing find the maximum value a) negative 2 b ) 6 c) 8 d) 7

Maximum value corresponds to the zero quadratic term in your case it is obviousely at x=-7 the maximum valu is then f(-7) = -2

Answer: a. negative

#7) find the x- and y -intercepts if no intercepts say so.

f (x) -2x^2 + 3x -27

a) x- intercepts ( -9,0 and 3/2) and y intercept 0,27)

b) x- intercepts 3,0, and -9/2) y=0,-27 c) x= 3,0

a) x- neg9,0 and 3/2 y-0,27

B) x- 3,0, and -9/2 y- 0 -27

c) x-3,0 and 9/2 y-0,27

d) x-9,0 and -3/2 y- 0,and -27.

solving the equation below to find x-intercepts

-2x^2 + 3x -27=0

You get

again you have negative under the radical sign , so there is no intercept.

For y-intercept it is easy just replace f(0) = -27 I do not see how it matches you answers please check the problem.

Answer: there is no x-intercept and the y- intercept is y=-27

#8 Approx how far will an object fall in 4 secs. if it is thrown downward at an initial velocity of 20 meters per sec using formula 4.9t^2 + Vot = S

S= 4.9t^2 + Vot = 4.9*(4)^2 + 20*4 = 158

Answer: 158 meters

#9) Translate the problem into a pair of linear equations in two variables Solve the equations using either elimination or substitution. S tate yuor answer for the specified variable.

A sum of money amounting to $ 3.80 consists of dimes and quarters. If there are 20 coins in all, how many are quarters?

Denote by

x—number of quarters.

y—number of dime.

You have the following equations:

X+y=20

25x+10y=380

Solve first equation for x: x=20-y

Substituting into second equation you get:

25*(20-y)+10y=380  500-25y+10y = 380  500-15y=380 15y=120  y=8

Now you find x as x=20-y=20-8=12

Answer: 12 quarters and 8 dimes.