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Diego wrote f(x)=(x+2)(x−4) as an example of a function whose graph has x-intercepts at x=−4, 2. What was his mistake?

Respuesta :

lucycruz626
the x-intercepts would be
x= -2 and x=4
His mistake was that he didn’t solve for x. To solve for x:
x+2=0
x=-2
and
x-4=0
x=4
CintiaSalazar

Taking into account the factored form, Diego's mistake was to express the opposite signs to those he should have.

The function f(x) = ax²  + bx + c

with a, b, c real numbers and a ≠ 0, is a function  quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).

The following expression is called discriminant:

Δ= b²- 4*a*c

The discriminant determines the amount of  roots of the function. The roots are those values ​​of x for which the expression is 0, so it graphically cuts the x-axis.

Then:

  • If Δ <0 the function has no real roots and its graph does not intersect the x-axis.
  • If Δ> 0 the function has two real roots and its graph intersects the x-axis at two points .
  • If Δ = 0 the function has a real root and its graph intersects the x-axis at a single point that coincides with its vertex. In this case the function is said to have a double root.

Every quadratic function can be factored based on its roots as:

f(x)= a(x-x1)(x-x2)

where x1 and x2 are the roots of the function. This way of expressing the quadratic function is called the factored form.

If the function does not have real roots (Δ <0) it cannot be factored, that is, it does not have a factored form.

If the function has a double real root (Δ = 0) the factored function takes the form:

f(x)= a(x-x1)²

In this case, the function has x-intercepts at x=−4, 2. So, an example of the factored form is:

f(x)=[x-(+2)][x-(-4)]

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

Finally, Diego's mistake was to express the opposite signs to those he should have.

Learn more:

https://brainly.com/question/14477557?referrer=searchResults

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