DSAT Advanced Math 4

Question 1

Which of the following equations represents a parabola with vertex at (-1, 4) that opens downward?

Accepted Answer

y = -(x+1)² + 4

Answer

Vertex form is y = a(x-h)² + k; vertex (-1,4) means h=-1,k=4; opens down means a<0: y = -(x+1)² + 4.

Question 2

Simplify: (27x⁶)^(1/3)

Accepted Answer

3x²

Answer

27^(1/3) = 3 and (x⁶)^(1/3) = x², so the answer is 3x².

Question 3

A function is defined by f(x) = (x² - 4) / (x - 2). What value does f(x) approach as x approaches 2?

Accepted Answer

4

Answer

Factor numerator as (x-2)(x+2), cancel (x-2), and as x→2 the expression approaches 2+2=4.

Question 4

The equation x² + y² = 25 represents a circle. Which point lies on this circle?

Accepted Answer

(3, 4)

Answer

Check (3,4): 3² + 4² = 9 + 16 = 25. ✓

Question 5

If x - 1/x = 3, what is x² + 1/x²?

Accepted Answer

11

Answer

Square both sides: x² - 2 + 1/x² = 9, so x² + 1/x² = 11.

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