Question

Select ALL the correct answers.

Consider the following quadratic equation.
y=x²-8x+4
Which of the following statements about the equation are true?

When y = 0, the solutions of the equation are x=8±2√2.
The extreme value of the graph is at (8,-4).
When y = 0, the solutions of the equation are x=4±2√3.
The extreme value of the graph is at (4,-12).
The graph of the equation has a minimum.
The graph of the equation has a maximum.

Answer 1

Statements 3, 4 and 5 are true.

Explanation:

x^2 - 8x + 4

Using the quadratic formula:

x = [ -(-8) +/- √((-8)^2 - 4*1*4)] / 2

= (8 +/- √(64 - 16)) / 2

= 4 +/- √48 / 2

= 4 +/- 4√3/2

= 4 +/- 2√3.

So the third statement is true.

Converting to vertex form:

x^2 - 8x + 4

= (x - 4)^2 - 16 + 4

= (x - 4)^2 -12

So the extreme value is at (4, -12)

So the fourth statement is true.

The coefficient of the term in x^2 is 1 (positive) so the graph has a minimum.