Quadratic functions

Question 1

what is the general form of a quadratic function in terms of f(x)

Answer 1

f(x)= ax^2 + bx + c where a,b,c are constants and a ≠ 0

Question 2

what is the general way to expand quadratics in the form (ax + b)^2

Answer 2

a^2x^2 + 2abx + b^2

Question 3

state the quadratic formula

Answer 3

The solutions of ax^2+bx+c =0 where a ≠ 0 are given by the formula

x= −b±√b^2-4ac/2a

Question 4

if the graph in the form y = ax^2 + bx + c is positive, what is the value of a?

Answer 4

a>0

Question 5

if the graph in the form y = ax^2 + bx + c is negative, what is the value of a?

Answer 5

a<0

Question 6

At what point of a quadratic function in the form y = ax^2 + bx + c does the function cross the y-axis?

Answer 6

(0,c)

Question 7

At what point of a quadratic function in the form y = ax^2 + bx + c does the function cross the x-axis?

Answer 7

The solutions to the equation
ax^2 + bx + c = 0

Question 8

describe the process of completing the square on a function in the form x^2 + bx + c

Answer 8

1.) Half the coefficient of x and put it into the bracket in the form (x+b/2)^2
2.) subtract (b/2)^2
3.) add the constant
the function should end up in the form (x+p)^2+q

Question 9

describe the process of completing the square on a function in the form ax^2 + bx + c

Answer 9

1.) factor out the a from both the value of x^2 and x
2.)Half the coefficient of x and put it into the bracket in the form (x+b/2)^2
3.) subtract (b/2)^2
4.) factor back in the value of a
5.) add the constant
the function should end up in the form a(x+p)^2+q

Question 10

for a quadratic function in the form a(x + p)^2+q, where is the turning point?

Answer 10

(-p,q)

Question 11

When solving quadratic inequalities, what one thing should you always do to eliminate all mistakes?

Answer 11

Sketch a graph of the function

Question 12

What is the discriminant of a quadratic function

Answer 12

the value of b^2-4ac in the quadratic equation

Question 13

if the discriminant = 0, how many real solutions does the quadratic have?

Answer 13

1 repeated solution

Question 14

if the discriminant < 0, how many real solutions does the quadratic have?

Answer 14

0 (2 imaginary roots)

Question 15

if the discriminant > 0, how many real solutions does the quadratic have?

Answer 15

2

Question 16

For the equation, x^4 - 3x^2 - 4 = 0, what substitution needs to be made to crate a disguised quadratic function

Answer 16

y=x^2