11. The given parabola has equation: ![f(x)=-3x^2-18x-35](https://tex.z-dn.net/?f=f%28x%29%3D-3x%5E2-18x-35)
We complete the square to have the function in the vertex form: ![f(x)=-3(x^2+6x)-35](https://tex.z-dn.net/?f=f%28x%29%3D-3%28x%5E2%2B6x%29-35)
![f(x)=-3(x^2+6x+9)+3*9-35](https://tex.z-dn.net/?f=f%28x%29%3D-3%28x%5E2%2B6x%2B9%29%2B3%2A9-35)
![f(x)=-3(x^2+6x+9)+27-35](https://tex.z-dn.net/?f=f%28x%29%3D-3%28x%5E2%2B6x%2B9%29%2B27-35)
![f(x)=-3(x+3)^2-8](https://tex.z-dn.net/?f=f%28x%29%3D-3%28x%2B3%29%5E2-8)
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
is a parabola that opens up and has its minimum point at the origin.
The range of this function is ![y\ge 0](https://tex.z-dn.net/?f=y%5Cge%200)
A straight line that has its y-intercept below the x-axis (y=3x-6) will not intersect
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](https://tex.z-dn.net/?f=x%5E2%2B21x%3D5x-63)
![x^2+21x-5x+63=0](https://tex.z-dn.net/?f=x%5E2%2B21x-5x%2B63%3D0)
![x^2+16x+63=0](https://tex.z-dn.net/?f=x%5E2%2B16x%2B63%3D0)
The factored form is ![(x+7)(x+9)=0](https://tex.z-dn.net/?f=%28x%2B7%29%28x%2B9%29%3D0)
![x=-7\:or\: x=-9](https://tex.z-dn.net/?f=x%3D-7%5C%3Aor%5C%3A%20x%3D-9)
Ans: C. x = −7, −9
15. The given quadratic expression is ![6x^2-17x+10](https://tex.z-dn.net/?f=6x%5E2-17x%2B10)
We split the middle term to obtain:
![6x^2-12x-5x+10=0](https://tex.z-dn.net/?f=6x%5E2-12x-5x%2B10%3D0)
We factor by grouping to get:
![6x(x-2)-5(x-2)=0](https://tex.z-dn.net/?f=6x%28x-2%29-5%28x-2%29%3D0)
Ans: D. 6x − 5