MATH SOLVE

2 months ago

Q:
# Which of the following statements are true about the equation below?

Accepted Solution

A:

Given: x^2 - 6x + 2

Statements:

1) The graph of the quadratic equation has a minimum value:TRUE. WHEN THE COEFFICIENT OF X^2 IS POSITIVE THE PARABOLA OPEN UPWARDS AND ITS VERTEX IS THE MINIMUM.

2) The extreme value is at the point (3 , - 7): TRUE

You have to find the vertex of the parabola:

x^2- 6x + 2 = (x - 3)^2 - 9 + 2 = (x - 3)^2 - 7 => vertex = (3, -7)

3) The extreme value is at the point (7, -3): FALSE. THE RIGHT VALUE WAS FOUND IN THE PREVIOUS POINT.

4) The solutions are x = - 3 +/- √7. FALSE.

Solve the equation:

(x - 3)^2 - 7 = 0 => (x - 3)^2 = 7 => (x - 3) = +/- √7 => x = 3 +/- √7

5) The solutions are x = 3 +/- √7. TRUE (SEE THE SOLUTION ABOVE).

6) The graph of the quadratic equation has a maximum value: FALSE (SEE THE FIRST STATEMENT).

Statements:

1) The graph of the quadratic equation has a minimum value:TRUE. WHEN THE COEFFICIENT OF X^2 IS POSITIVE THE PARABOLA OPEN UPWARDS AND ITS VERTEX IS THE MINIMUM.

2) The extreme value is at the point (3 , - 7): TRUE

You have to find the vertex of the parabola:

x^2- 6x + 2 = (x - 3)^2 - 9 + 2 = (x - 3)^2 - 7 => vertex = (3, -7)

3) The extreme value is at the point (7, -3): FALSE. THE RIGHT VALUE WAS FOUND IN THE PREVIOUS POINT.

4) The solutions are x = - 3 +/- √7. FALSE.

Solve the equation:

(x - 3)^2 - 7 = 0 => (x - 3)^2 = 7 => (x - 3) = +/- √7 => x = 3 +/- √7

5) The solutions are x = 3 +/- √7. TRUE (SEE THE SOLUTION ABOVE).

6) The graph of the quadratic equation has a maximum value: FALSE (SEE THE FIRST STATEMENT).