SAT Math: Complete the Square

1. $f(x)=(x+3)(x-1)$

Which of the following is an equivalent form of the function $f$ above in which the minimum value of $f$ appears as a constant or coefficient?

$f(x)=x^2 -3$

$f(x)=x^2 +2x-3$

$f(x)=(x+1)^2 -4$

$f(x)=(x-1)^2 +3$

2. $y=x^2+ 12x+20$

The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x-intercepts of the parabola as constants or coefficients?

$y-20=x^2 +12$

$y+2=(x+10)^2$

$y=x(x+6)+16$

$y=(x+6)^2 -16$

3. $f(x)=(x+2)(x+6)$

Which of the following is an equivalent form of the function $f$ above in which the maximum value of $f$ appears as a constant or coefficient?

$f(x)=(x+2)^2 +6$

$f(x)=x^2 +8x+12$

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

$f(x)= (x+2)^2 -16$

4. $f(x)=x^2 +2x-63$

The function above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x-intercepts of the parabola as constants or coefficients?

$f(x)=(x-7)(x+9)$

$f(x)=(x+1)^2 -64$

$f(x)= (x-1)^2 +9$

$f(x)=(x+9)-7$

5. $y=x^2 -8x-48$

Which of the following is an equivalent form of the equation above in which the minimum value of $f$ appears as a constant or coefficient?

$y=(x-12)(x+4)$

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

$y=(x-4)^2 -64$

$y=(x+4)^2 -56$

6. $y=2x^2 -4x+5$

The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x-intercepts of the parabola as constants or coefficients?

$y=2(x-1)^2 +3$

$y=(x-3)^2 +2$

$y=(x+1)^2 -3$

$y=2(x-1)^2$

SAT Math: Complete the Square – Vertex Form 2