The vertex form allows us to identify, very easily, the vertex of the parabola and hence its name.

**The vertex form of the quadratic function is:**

$Y=a(X-p)^2+c$

The vertex form allows us to identify, very easily, the vertex of the parabola and hence its name.

**The vertex form of the quadratic function is:**

$Y=a(X-p)^2+c$

\( f(x)=(x-3)^2+x \)

Where the values of the vertex of the parabola are $( p,c)$

$P$ - represents the value of the $X$ of the vertex.

$C$ - represents the value of the $Y$ of the vertex.

For example in the function:

$Y=2(X-3)^2+5$

The vertex of the parabola is:

$(3,5)$

**Observe**

In the formula for the vertex form there is a minus sign before $P$. This is how the template is constructed, it does not mean that $P$ is negative.

If we obtain a negative $X$ vertex we will place it with a minus sign in the vertex form template and the minus will turn into plus.

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

$f(x)=x^2-5x+9$

Find the standard representation of the following function

$f(x)=(2x+1)^2-1$

$f(x)=4x^2+4x$

Find the standard representation of the following function

$f(x)=(-x+1)^2+3$

$f(x)=x^2-2x+4$

Find the standard representation of the following function

$f(x)=(x+4)^2-16$

$f(x)=x^2+8x$

Find the standard representation of the following function

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

$f(x)=x^2-4x+7$

Test your knowledge

Question 1

Find the standard representation of the following function

\( f(x)=(2x+1)^2-1 \)

Question 2

Find the standard representation of the following function

\( f(x)=(-x+1)^2+3 \)

Question 3

Find the standard representation of the following function

\( f(x)=(x+4)^2-16 \)

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
- Standard Form of the Quadratic Function
- 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)