Standard Form of the Quadratic Function

🏆Practice standard representation

Standard Form of the Quadratic Function

The standard form of the quadratic function is:
Y=ax2+bx+cY=ax^2+bx+c

For example:
Y=4x2+3x+15Y=4x^2+3x+15

Start practice

Test yourself on standard representation!

einstein

Choose the correct algebraic expression based on the parameters:

\( a=-3,b=3,c=7 \)

Practice more now

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 XX vertex.
  • Let's find the YY vertex.
  • Let's place in the vertex form template the X X vertex instead of PP, the YY vertex instead of CC and the aa instead of aa.

How do you go from standard form to factored form?

  • Let's find the points of intersection of the parabola with the xx 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 X2X^2 we will place it in the factoring formula before locating the intersection points there, as follows:

y=a×(xt)×(xk) y=a\times(x-t)\times(x-k)


Examples and exercises with solutions of the Standard form of the quadratic function

Exercise #1

Find the standard representation of the following function

f(x)=(x2)(x+5) f(x)=(x-2)(x+5)

Video Solution

Step-by-Step Solution

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

(a+1)⋆(b+2) = ab+2a+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!

Answer

f(x)+x2+3x10 f(x)+x^2+3x-10

Exercise #2

Choose the correct algebraic expression based on the parameters:

a=3,b=3,c=7 a=-3,b=3,c=7

Video Solution

Answer

3x2+3x+7 -3x^2+3x+7

Exercise #3

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

x2x1 -x^2-x-1

Exercise #4

Create an algebraic expression based on the following parameters:

a=0,b=1,c=0 a=0,b=1,c=0

Video Solution

Answer

x x

Exercise #5

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

x2 -x^2

Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge
Start practice