The standard form of the quadratic function is:

$Y=ax^2+bx+c$

For example:

$Y=4x^2+3x+15$

The standard form of the quadratic function is:

$Y=ax^2+bx+c$

For example:

$Y=4x^2+3x+15$

Create an algebraic expression based on the following parameters:

\( a=-1,b=-1,c=-1 \)

How do you go from standard form to vertex form?

- We need to find the vertex of the parabola using the formula to find the $X$ vertex.
- Let's find the $Y$ vertex.
- Let's place in the vertex form template the $X$ vertex instead of $P$, the $Y$ vertex instead of $C$ and the $a$ instead of $a$.

How do you go from standard form to factored form?

- Let's find the points of intersection of the parabola with the $x$ axis.
- Let's place it in the factored form template.

**Look!**

If we were to realize that in the standard form there is a coefficient for $X^2$ we will place it in the factoring formula before locating the intersection points there, as follows:

$y=a\times(x-t)\times(x-k)$

Find the standard representation of the following function

$f(x)=(x-2)(x+5)$

We will begin by using the distributive property in order to expand the following expression.

(*a*+1)⋆(*b*+2) = *ab*+2*a*+*b*+2

We will then proceed to insert the known values into the equation and solve as follows:

(x-2)(x+5) =

x²-2x+5x+-2*5=

x²+3x-10

And that's the solution!

$f(x)+x^2+3x-10$

Create an algebraic expression based on the following parameters:

$a=-1,b=-1,c=-1$

$-x^2-x-1$

Create an algebraic expression based on the following parameters:

$a=3,b=0,c=-3$

$3x^2-3$

Create an algebraic expression based on the following parameters:

$a=1,b=-1,c=1$

$x^2-x+1$

Create an algebraic expression based on the following parameters:

$a=-1,b=-8,c=0$

$-x^2-8x$

Test your knowledge

Question 1

Create an algebraic expression based on the following parameters:

\( a=3,b=0,c=-3 \)

Question 2

Create an algebraic expression based on the following parameters:

\( a=1,b=-1,c=1 \)

Question 3

Create an algebraic expression based on the following parameters:

\( a=-1,b=-8,c=0 \)

Related Subjects

- Quadratice Equations and Systems of Quadraric Equations
- Quadratic Equations System - Algebraic and Graphical Solution
- Solution of a system of equations - one of them is linear and the other quadratic
- Intersection between two parabolas
- Word Problems
- Properties of the roots of quadratic equations - Vieta's formulas
- Ways to represent a quadratic function
- Various Forms of the Quadratic Function
- Vertex form of the quadratic equation
- Factored form of the quadratic function
- The quadratic function
- Quadratic Inequality
- Parabola
- Symmetry in a parabola
- Plotting the Quadratic Function Using Parameters a, b and c
- Finding the Zeros of a Parabola
- Methods for Solving a Quadratic Function
- Completing the square in a quadratic equation
- Squared Trinomial
- The quadratic equation
- Families of Parabolas
- The functions y=x²
- Family of Parabolas y=x²+c: Vertical Shift
- Family of Parabolas y=(x-p)²
- Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts)