Question

11. What is the location of the vertex of the parabola defined by f(x) = −3x2 − 18x − 35 and in what direction does the parabola open?

A. Vertex: (2, −12), opens upward


B. Vertex: (−3, −8), opens downward


C. Vertex: (3, 8), opens downward


D. Vertex: (−3, 8), opens downward



12. Graph the following systems of equations. Which system has no solution?


A. y equals x squared, y equals 3x plus 3


B. y equals x squared, y equals 3x plus 1


C. y equals x squared, y equals 3x


D. y equals x squared, y equals 3x minus 6



14. Determine the zeros of x2 + 21x = 5x − 63.


A. x = 7, −9


B. x = −7, 9


C. x = −7, −9


D. x = 0, −7, −9



15. What is one factor of 6x2 − 17x + 10?


A. 3x − 5


B. 4x − 3


C. 8x + 3


D. 6x − 5



16. What are the zeros for the function f(x) = 2x2+ 20x + 68 and how many times does the graph cross the x-axis?


A. x = −5 ± 3i, never


B. x equals start fraction five over two end fraction plus or minus start fraction one over two end fraction i comma two times


C. x = 5 ± 14i, two times


D. x = −5 ± i, one time



17. When solving x2 + 10x − 7 = 0 by completing the square, which of the following is a step in the process?


A. (x − 5)2 = 32


B. (x + 5)2 = 18


C. (x − 5)2 = 18


D. (x + 5)2 = 32



19. Solve 2x2 + 5x − 6 = 0 using the quadratic formula.


A. x equals start fraction negative five plus or minus square root of 23 end square root over four end fraction


B. x equals start fraction five plus or minus square root of 23 end square root over four end fraction


C. x equals start fraction negative five plus or minus square root of 73 end square root over four end fraction


D. x equals start fraction five plus or minus square root of 73 end square root over four end fraction



22. Solve 2x2 + 16x + 27 = 0 by completing the square.


A. x equals four plus or minus square root of start fraction five over two end fraction end square root


B. x equals four plus or minus square root of five end square root


C. x equals negative four plus or minus square root of start fraction five over two end fraction end square root


D. x equals negative four plus or minus square root of five end square root



23. Use completing the square to rewrite y = x2 + 4x − 13 in vertex form, then identify the maximum or minimum value.


A. Minimum: −17


B. Maximum: −2


C. Minimum: −13


D. Maximum: −13

Answer 1

11. The given parabola has equation:
`f(x)=-3x^2-18x-35`

We complete the square to have the function in the vertex form:
`f(x)=-3(x^2+6x)-35`

`f(x)=-3(x^2+6x+9)+3*9-35`

`f(x)=-3(x^2+6x+9)+27-35`

`f(x)=-3(x+3)^2-8`

The vertex is (-3,-8), the graph opens down because a=-3<0

Ans: B. Vertex: (−3, −8), opens downward

12. We know the graph of
`y=x^2` is a parabola that opens up and has its minimum point at the origin.

The range of this function is
`y\ge 0`

A straight line that has its y-intercept below the x-axis (y=3x-6) will not intersect
`y=x^2` and hence will form a system with no solution.

Ans: D. y equals x squared, y equals 3x minus 6

14. We want to find the zeros of
`x^2+21x=5x-63`

`x^2+21x-5x+63=0`

`x^2+16x+63=0`

The factored form is
`(x+7)(x+9)=0`

`x=-7\:or\: x=-9`

Ans: C. x = −7, −9

15. The given quadratic expression is
`6x^2-17x+10`

We split the middle term to obtain:

`6x^2-12x-5x+10=0`

We factor by grouping to get:

`6x(x-2)-5(x-2)=0`

`(x-2)(6x-5)=0`

Ans: D. 6x − 5