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:

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

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:

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

Test your knowledge

Question 1

Create an algebraic expression based on the following parameters:

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

Question 2

Create an algebraic expression based on the following parameters:

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

Question 3

Create an algebraic expression based on the following parameters:

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

Related Subjects

- The quadratic function
- Parabola
- Symmetry in a parabola
- Quadratic Inequality
- 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)
- Vertex form of the quadratic equation
- Factored form of the quadratic function
- Completing the square in a quadratic equation
- Various Forms of the Quadratic Function
- Quadratice Equations and Systems of Quadraric Equations
- Quadratic Equations System - Algebraic and Graphical Solution
- Squared Trinomial
- Word Problems