The Quadratic Formula: Identifying and defining elements

Question 1

a = coefficient of x²

b = coefficient of x

c = coefficient of the constant term

What is the value of $$ c $$ in the function $$ y=-x^2+25x $$ ?

Question 2

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$$ 5-6x^2+12x=0 $$

What are the components of the equation?

Question 3

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$$ 10x^2+5+20x=0 $$

What are the components of the equation?

Question 4

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$$ -8x^2-5x+9=0 $$

What are the components of the equation?

Question 5

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$$ -x^2-2=0 $$

What are the components of the equation?

Examples with solutions for The Quadratic Formula: Identifying and defining elements

Exercise #1

a = coefficient of x²

b = coefficient of x

c = coefficient of the constant term

What is the value of $c$ in the function $y=-x^2+25x$ ?

Video Solution

Step-by-Step Solution

Let's recall the general form of the quadratic function:

$y=ax^2+bx+c$ The function given in the problem is:

$y=-x^2+25x$ $c$ is the free term (meaning the coefficient of the term with power 0),

In the function in the problem there is no free term,

Therefore, we can identify that:

$c=0$ Therefore, the correct answer is answer A.

Answer

$c=0$

Exercise #2

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$5-6x^2+12x=0$

What are the components of the equation?

Video Solution

Answer

$a=-6$ $b=12$ $c=5$

Exercise #3

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$10x^2+5+20x=0$

What are the components of the equation?

Video Solution

Answer

$a=10$ $b=20$ $c=5$

Exercise #4

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$-8x^2-5x+9=0$

What are the components of the equation?

Video Solution

Answer

$a=-8$ $b=-5$ $c=9$

Exercise #5

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$-x^2-2=0$

What are the components of the equation?

Video Solution

Answer

$a=-1$ $b=0$ $c=-2$

Question 1

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$$ x^2+4x-5=0 $$

What are the components of the equation?

Question 2

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$$ x^2+7x=0 $$

What are the components of the equation?

Question 3

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

Question 4

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

Identifies a,b,c

$$ 5x^2+6x-8=0 $$

Question 5

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $$ c $$ in this quadratic equation:

$$ y=-5x^2+4x-3 $$

Exercise #6

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$x^2+4x-5=0$

What are the components of the equation?

Video Solution

Answer

$a=1$ $b=4$ $c=-5$

Exercise #7

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$x^2+7x=0$

What are the components of the equation?

Video Solution

Answer

$a=1$ $b=7$ $c=0$

Exercise #8

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $a$ in the equation

$y=3x-10+5x^2$

Video Solution

Answer

$a=5$

Exercise #9

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

Identifies a,b,c

$5x^2+6x-8=0$

Video Solution

Answer

$a=5$ $b=6$ $c=-8$

Exercise #10

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $c$ in this quadratic equation:

$y=-5x^2+4x-3$

Video Solution

Answer

$c=-3$

Question 1

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=-x^2-3x+1 $$

Question 2

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $$ b $$ in the equation

$$ y=2x-3x^2+1 $$

Question 3

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ b $$ in the equation

$$ y=3x^2+10-x $$

Question 4

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $$ b $$ in this quadratic equation:

$$ y=4x^2-16 $$

Question 5

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $$ c $$ in this quadratic equation:

$$ y=5+3x^2 $$

Exercise #11

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $a$ in the equation

$y=-x^2-3x+1$

Video Solution

Answer

$a=-1$

Exercise #12

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $b$ in the equation

$y=2x-3x^2+1$

Video Solution

Answer

$b=2$

Exercise #13

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $b$ in the equation

$y=3x^2+10-x$

Video Solution

Answer

$b=-1$

Exercise #14

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $b$ in this quadratic equation:

$y=4x^2-16$

Video Solution

Answer

$b=0$

Exercise #15

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $c$ in this quadratic equation:

$y=5+3x^2$

Video Solution

Answer

$c=5$

Question 1

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $$ a $$ in this quadratic equation:

$$ y=3x+30 $$

Question 2

What is the value of $$ a $$ in the equation $$ 4x^2=-4x+16 $$ ?

Exercise #16

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $a$ in this quadratic equation:

$y=3x+30$

Video Solution

Answer

That's not a quadratic equation

Exercise #17

What is the value of $a$ in the equation $4x^2=-4x+16$ ?

Video Solution

Answer

$a=4$