- What are the
*x*-intercepts of *y*=(*x*−2)(*x*+5) ?

- A. (0, 2) and (0, -5)
- B. (0, -2) and (0, 5)
- C. (-2, 0) and (5, 0)
- D. (2, 0) and (-5, 0)

answer is D

X-2=>

X=2 (2,0)

X+5=0

X=-5 (-5,0)

Correct or not

Yes, that is correct. An "x- intercept" is a point on the graph where the graph crosses ("intersects") the x-axis. There y= 0. If y= (x- 2)(x+ 5)= 0 then either x- 2= 0 or x+ 5= 0. If x- 2= 0 then x= 2. If x+ 5= 0 then x= -5. In either case y= 0 so the x-intercepts are (2, 0) and (-5, 0).

- Which of these quadratic functions has exactly one
*x* -intercept?

- A.
*y*=*x* 2 −9
- B.
*y*=*x* 2 −6*x*+9
- C.
*y*=*x* 2 −5*x*+6
- D.
*y*=*x* 2 +*x*−6

MY ANSWER IS

A

(X-#)(X+3)

CORRECT OR NOT

No, that is

**not** correct

A. \(\displaystyle y= x^2- 9= (x- 3)(x+ 3)= 0\). We have either x- 3= 0 so x= -3 or x+ 3= 0 so x= -3. The

**two** x-intercepts are (3, 0) and (-3, 0).

B. \(\displaystyle y= x^2- 6x+ 9= (x- 3)^2= 0\). We must have x= 3. There is only one x-intercept.

C. \(\displaystyle y= x^2- 5x+ 6= (x- 3)(x- 2)= 0\). We must have either x- 3= 0 so x= 3 or x- 2= 0 so x= 2. The

**two** x-intercepts are (3, 0) and (2, 0).

D. \(\displaystyle y= x^2+ x- 6= (x+ 3)(x- 2)= 0\). We must have either x+ 3= 0 so x= -3 or x- 2= 0 so x= 2. The

**two** x-intercepts are (-3, 0) and (2, 0).

The correct answer is B.

- Which of the following parabolas opens upward and appears narrower than
*y*=−3*x* 2 +2*x*−1 ?

- A.
*y*= 4*x* 2 −2*x*−1
- B.
*y*= −4*x* 2 +2*x*−1
- C.
*y*=* x* 2 +4*x*

D.

*y*= −2

*x* 2 +

*x*+

MY ANSWER IS

A

CORRECT OR NOT

Yes, that is correct.

A parabola opens upward if and only if its leading coefficient (the coefficient of \(\displaystyle x^2\)) is positive. That is true in A and C. How "narrow" a parabola appears depends upon how large the absolute value of the leading coefficient is. The larger the leading coefficient, the "narrower" the parabola is. |4|= 4 is larger than |-3|= 3 while |1|= 1 is not.