The function y=ax²+bx+c: Matching parameters

Matching equations to graphsIdentifying and defining elementsDetermine the algebraic representation of the following descriptions
Question 1

\( y=x^2+10x \)

Question 2

\( y=2x^2-5x+6 \)

Question 3

\( y=x^2 \)

Question 4

\( y=x^2-6x+4 \)

Question 5

\( y=2x^2-3x-6 \)

Examples with solutions for The function y=ax²+bx+c: Matching parameters

Exercise #1

y=x2+10x y=x^2+10x

Video Solution

Step-by-Step Solution

Here we have a quadratic equation.

A quadratic equation is always constructed like this:

 

y=ax2+bx+c y = ax²+bx+c

 

Where a, b, and c are generally already known to us, and the X and Y points need to be discovered.

Firstly, it seems that in this formula we do not have the C,

Therefore, we understand it is equal to 0.

c=0 c = 0

 

a is the coefficient of X², here it does not have a coefficient, therefore

a=1 a = 1

 

b=10 b= 10

is the number that comes before the X that is not squared.

 

Answer

a=1,b=10,c=0 a=1,b=10,c=0

Exercise #2

y=2x2−5x+6 y=2x^2-5x+6

Video Solution

Step-by-Step Solution

In fact, a quadratic equation is composed as follows:

y = ax²-bx-c

 

That is,

a is the coefficient of x², in this case 2.
b is the coefficient of x, in this case 5.
And c is the number without a variable at the end, in this case 6.

Answer

a=2,b=−5,c=6 a=2,b=-5,c=6

Exercise #3

y=x2 y=x^2

Video Solution

Answer

a=1,b=0,c=0 a=1,b=0,c=0

Exercise #4

y=x2−6x+4 y=x^2-6x+4

Video Solution

Answer

a=1,b=−6,c=4 a=1,b=-6,c=4

Exercise #5

y=2x2−3x−6 y=2x^2-3x-6

Video Solution

Answer

a=2,b=−3,c=−6 a=2,b=-3,c=-6

Question 1

\( y=-2x^2+3x+10 \)

Question 2

\( y=3x^2+4x+5 \)

Question 3

\( y=x^2+x+5 \)

Question 4

\( y=-x^2+x+5 \)

Question 5

\( y=4+3x^2-x \)

Exercise #6

y=−2x2+3x+10 y=-2x^2+3x+10

Video Solution

Answer

a=−2,b=3,c=10 a=-2,b=3,c=10

Exercise #7

y=3x2+4x+5 y=3x^2+4x+5

Video Solution

Answer

a=3,b=4,c=5 a=3,b=4,c=5

Exercise #8

y=x2+x+5 y=x^2+x+5

Video Solution

Answer

a=1,b=1,c=5 a=1,b=1,c=5

Exercise #9

y=−x2+x+5 y=-x^2+x+5

Video Solution

Answer

a=−1,b=1,c=5 a=-1,b=1,c=5

Exercise #10

y=4+3x2−x y=4+3x^2-x

Video Solution

Answer

a=3,b=−1,c=4 a=3,b=-1,c=4

Question 1

\( y=3x^2+4-5x \)

Question 2

\( y=-4x^2-3x \)

Question 3

\( y=-x^2+3x+40 \)

Question 4

\( y=6x+3x^2-4 \)

Question 5

\( y=-5x^2+x \)

Exercise #11

y=3x2+4−5x y=3x^2+4-5x

Video Solution

Answer

a=3,b=−5,c=4 a=3,b=-5,c=4

Exercise #12

y=−4x2−3x y=-4x^2-3x

Video Solution

Answer

a=−4,b=−3,c=0 a=-4,b=-3,c=0

Exercise #13

y=−x2+3x+40 y=-x^2+3x+40

Video Solution

Answer

a=−1,b=3,c=40 a=-1,b=3,c=40

Exercise #14

y=6x+3x2−4 y=6x+3x^2-4

Video Solution

Answer

a=3,b=6,c=−4 a=3,b=6,c=-4

Exercise #15

y=−5x2+x y=-5x^2+x

Video Solution

Answer

a=−5,b=1,c=0 a=-5,b=1,c=0

Question 1

\( y=-x-3x^2 \)

Question 2

\( y=-6+x^2+6x \)

Question 3

\( y=-3x-4x^2+3 \)

Question 4

\( y=-5+x^2 \)

Question 5

\( y=2x^2+3 \)

Exercise #16

y=−x−3x2 y=-x-3x^2

Video Solution

Answer

a=−3,b=−1,c=0 a=-3,b=-1,c=0

Exercise #17

y=−6+x2+6x y=-6+x^2+6x

Video Solution

Answer

a=1,b=6,c=−6 a=1,b=6,c=-6

Exercise #18

y=−3x−4x2+3 y=-3x-4x^2+3

Video Solution

Answer

a=−4,b=−3,c=3 a=-4,b=-3,c=3

Exercise #19

y=−5+x2 y=-5+x^2

Video Solution

Answer

a=1,b=0,c=−5 a=1,b=0,c=-5

Exercise #20

y=2x2+3 y=2x^2+3

Video Solution

Answer

a=2,b=0,c=3 a=2,b=0,c=3