In this article, we will learn the three most common ways to solve a quadratic function easily and quickly.

In this article, we will learn the three most common ways to solve a quadratic function easily and quickly.

- Trinomial
- Quadratic Formula
- Completing the Square

The basic quadratic function equation is:

$Y=ax^2+bx+c$

When:

$a$ - the coefficient of $X^2$

$b$ - the coefficient of $X$

$c$ - the constant term

- $a$ must be different from $0$
- $b$ or $c$ can be $0$
- $a,b,c$ can be negative/positive
- The quadratic function can also look like this:
- $Y=ax^2$
- $Y=ax^2+bx$
- $Y=ax^2+c$

Question 1

Solve the following equation:

\( x^2+5x+4=0 \)

Question 2

\( x^2+9=0 \)

Solve the equation

Question 3

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 4

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 5

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?

Solve the following equation:

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

The parameters are expressed in the quadratic equation as follows:

aX2+bX+c=0

We substitute into the formula:

-5±√(5²-4*1*4)

2

-5±√(25-16)

2

-5±√9

2

-5±3

2

The symbol ± means that we have to solve this part twice, once with a plus and a second time with a minus,

This is how we later get two results.

-5-3 = -8

-8/2 = -4

-5+3 = -2

-2/2 = -1

And thus we find out that X = -1, -4

$x_1=-1$ $x_2=-4$

$x^2+9=0$

Solve the equation

The parameters are expressed in the quadratic equation as follows:

aX2+bX+c=0

We identify that we have:

a=1

b=0

c=9

We recall the root formula:

We replace according to the formula:

-0 ± √(0²-4*1*9)

2

We will focus on the part inside the square root (also called delta)

√(0-4*1*9)

√(0-36)

√-36

It is not possible to take the square root of a negative number.

And so the question has no solution.

No solution

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?

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

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?

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

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?

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

Question 1

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

Identifies a,b,c

\( 5x^2+6x-8=0 \)

Question 2

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 3

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?

Question 4

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 5

a = coefficient of x²

b = coefficient of x

c = coefficient of the constant term

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

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

Identifies a,b,c

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

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

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?

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

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?

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

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?

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

a = coefficient of x²

b = coefficient of x

c = coefficient of the constant term

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

$c=0$

Question 1

Solve the following equation:

\( x^2+9x+8=0 \)

Question 2

Solve the following equation:

\( -2x^2+22x-60=0 \)

Question 3

Solve the following equation:

\( 2x^2-10x-12=0 \)

Question 4

Solve the equation

\( 3x^2-39x-90=0 \)

Question 5

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of \( a \) in the equation

\( y=3x-10+5x^2 \)

Solve the following equation:

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

$x_1=-1$ $x_2=-8$

Solve the following equation:

$-2x^2+22x-60=0$

$x_1=5$ $x_2=6$

Solve the following equation:

$2x^2-10x-12=0$

$x_1=6$ $x_2=-1$

Solve the equation

$3x^2-39x-90=0$

$x_1=15$ $x_2=-2$

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $a$ in the equation

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

$a=5$