What are the coordinates of the vertex of the graph of the function -2(x - 1)2 = y + 5?

so the vertex is (1,5)

Determine Algebraically whether f(x) = 1 + x + x^2 is even, odd, or neither

A function is even if f(x) = f(-x), but for our function

f(-x)=1-x+x^2

so it is not even.

To be odd -f(x)=f(-x), and for our function

-f(x) = -1-x-x^2

and so it is also not odd.

Therefore it is neither.

without graphing, find the vertex and the maximum or minimum value of f(x) f(x) = -3/7 (x-8)^2+7

since f(x) is in this form, vertex is: (8,7) and since -3/7 < 0 the vertex is a maximum

Find the quadratic equation whose roots are twice the roots of 4x^2+8x-5=0.

ax^2+bx+c
4x^2+8x-5=0 
since a*c=-20 
we use 10 and -2 as follows 

4x^2+10x-2x-5=0 
2x(2x+5)-1(2x+5)=0 
(2x-1)(2x+5)=0 
so x=1/2 or x=-5/2 
and so 
(x-1)(x+5)=0 
x^2-6x-5=0 

:)

Derive a quadratic equation using the following points: (1, -4), (2, -5), (3, -10)

y = ax^2+bx+c 
(1) (1, -4) -> -4=a+b+c , 
(2) (2, -5) -> -5= 4a+2b+c, 
(3) (3, -10) -> -10=9a+3b+c 

(2)-(1): 
-5+4=4a-a+2b-b+c-c 
-1=3a+b (or 3a+b=-1) 
(3)-(1): 
-6=8a+2b (or 4a+b=-3) 

taking the difference of these 2 we get 

4a-3a+b-b=-3+1 (or a=-2) 

and thus b=5 
Now from (1):
-4=-2+5+c (so c=-7) 



y=-2x^2+5x+-7 

:) 

Find all integers m for which y^2+my+50 can be factored.

factors of 50:
1, 50
2, 25
5, 10 
So m can be 
{51, -51, 27, -27, 15, -15} 

:)

What is the maximum y value for f(x)= -x^2+8x+9

Vertex Formula: 
 

for each of the following find: A) the vertex, B)the y intercept, C) the x intercept of f(x)=(x-1)^2-2

This parabola is in standard form - which is nice: 
 
 
 


so our vertex is (1,-2) 

to get the y-intercept set x=0, then 


 

to get the x-intercept set f(x)=0, then 

 
 


 

so that 
x-1=2 or x-1=-2
x=0 or x=-1 

x-intercepts: {0, -1} 

:)

what is the number of real solutions in -x^2+9x+7=0

We can use the discriminant to determine the number and type of solutions: 

since the discriminant is real and not 0 we know that there are 2 real solutions

:)

Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 3 km an hour faster than the other. If after one hour the vehicles are 15 km apart, find the rate of each vehicle.

 
 
 
divide by 2... 
 
 

so the slower is 9 km an hour 
and the faster is 12 km per hour

for what values of k will x^2+k=0, have two nonreal solutions

If we subtract k from both side we get:

this equation will have two, non-real (imaginary) solutions for any real, positive number.
:)

use the method of completing the square to solve for x 3x^2-2x-1=0

so x=-1/3 or 1

Finding Axis of symmetry

f(x) = (x − 5)2 + 2 i need a axis of symmetry

Your Answer:

If by f(x) = (x − 5)2 + 2
you mean:



then we can use the fact that this equation is in standard form. This means that



gives us what we need to determine the axis of symmetry.
Therefore the axis of symmetry is:

x=5

:)

Factoring Quadratics expressions,

Factoring quadratics usually gives students headaches, bu it does not have to be this way. Let's go over some facts that will help us. 

• Not every quadratic can be factored into binomials (unless you factor over the complex numbers) 
• Factoring may be sometimes called finding the zeros, or solving for x
• Special factoring identities are very useful - so try them first
• There are several valid factoring methods but they all depend on finding a pair of factors of the product of the coefficients a and c and that add to the coefficient b 

I have been posting several factoring examples, look for them under the labels factoring, factoring polynomials, factoring quadratics, etc.

Complete the square

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

d² + 14d +

Solution:

So we add 49 to get a perfect square