Question

Match each quadratic function given in factored form with its equivalent standard form listed on the left. f(x) = (x + 2)(x – 6) f(x) = (x – 4)(x + 3) f(x) = (x – 12)(x + 1) f(x) = (x – 3)(x + 4)

Answer 1

Step-by-step explanation:

Write the standard form for the given factored form of quadratic functions

f(x) = (x + 2)(x – 6)

to get standard form we multiply the parenthesis using FOIL method

$f(x)=(x + 2)(x – 6)= x^2 -6x+2x-12= x^2-4x-12$

f(x) = (x – 4)(x + 3)

$f(x)=(x – 4)(x + 3)= x^2 +3x-4x-12= x^2-x-12$

f(x) = (x – 12)(x + 1)

$f(x)= (x – 12)(x + 1)=(x^2 +1x-12x-12= x^2-11x-12$

f(x) = (x – 3)(x + 4)

$f(x)=(x – 3)(x + 4)= x^2 +4x-3x-12= x^2+x-12$

Answer 2

The standard form of the given quadratic functions in factored form are:

$(x + 2)(x - 6) = x^2 - 4x - 12$

$(x – 4)(x + 3) = x^2 - x - 12$

$(x – 12)(x + 1) = x^2 - 11x - 12$

$(x – 3)(x + 4) = x^2 + x - 12$

What are quadratic functions?

A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is:

$\rm f(x)=ax^2+bx+c$, where a and b are not equals zero.

To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry addition or subtraction operations to obtain the equation.

We will begin with converting the first equation into standard form.

$ f(x) = (x + 2)(x – 6)\\f(x) = x(x – 6) + 2(x – 6)\\f(x) = x^2 - 6x + 2x -12\\f(x)  x^2 - 4x - 12$

Similarly the standard forms for equation 2, 3, and 4 are:

$(x – 4)(x + 3) = x^2 - x - 12$

$(x – 12)(x + 1) = x^2 - 11x - 12$

$(x – 3)(x + 4) = x^2 + x - 12$

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