Standard Form of the Quadratic Function

Standard Representation - Examples, Exercises and Solutions

Standard Form of the Quadratic Function

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

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

Detailed explanation

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Test yourself on standard representation!

einstein

Choose the correct algebraic expression based on the parameters:

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

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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:

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

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

Exercise #1

Find the standard representation of the following function

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

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

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

Exercise #2

Choose the correct algebraic expression based on the parameters:

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

Video Solution

Answer

$-3x^2+3x+7$

Exercise #3

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

$-x^2-x-1$

Exercise #4

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

$x$

Exercise #5

Create an algebraic expression based on the following parameters:

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

Video Solution

Answer

$-x^2$

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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:

$\( a=0,b=1,c=0 \)$

Question 3

Create an algebraic expression based on the following parameters:

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

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