Question
The graph of a linear equation and the graph of a quadratic equation are shown. What is true about the point (−1,4)?
- The point satisfies only the quadratic equation
- The point satisfies only the linear equation.
- The point satisfies both equations.
- The point satisfies neither equation.
Answer/Explanation
Ans: C
Question
\(y=(x+3)(x-7)\)
\(y=x-7\)
If \((x,y)\) is a solution to the given system of equations, which of the following could be the value of \(x\)?
- -7
- -3
- 3
- 7
Answer/Explanation
Ans: D
Question
A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the \(xy\)-plane above. How many solutions does the system have?
- 0
- 1
- 2
- 3
Answer/Explanation
Ans: C
Question
In the \(xy\)-plane, a parabola has vertex (3, 1) and intersects the \(x\)-axis at two points. If the equation of the parabola is written in the form \(y = ‐ax^2 +bx + c\), where \(a, b\), and \(c\) are constants, which of the following could be a value of \(c\)?
- -8
- 2
- 3
- 7
Answer/Explanation
Ans: A
Question
In the \(xy\)-plane, what is the \(y\)-coordinate of the point of intersection of the graphs of \(y = (x ‐ 1)^2\) and \(y = 2x ‐ 3\)?
Answer/Explanation
Ans: 1
Question
\(x-y=1\)
\(x+ y=x^2 -3\)
Which ordered pair is a solution to the system of equations above?
- \((1+\sqrt{3},3)\)
- \((\sqrt{3},-\sqrt{3})\)
- \((1+\sqrt{5},\sqrt{5})\)
- \((\sqrt{5},-1+\sqrt{5})\)
Answer/Explanation
Ans: A
Question
\((x+2)^2+(y-3)^2=40\)
\(y=-2x+4\)
Which of the following could be the \(x\)-coordinate of a solution to the system of equations above?
- \(\sqrt{7}\)
- \(\frac{\sqrt{35}}{2}\)
- \(\frac{6+2\sqrt{34}}{5}\)
- \(\frac{4+\sqrt{191}}{5}\)
Answer/Explanation
Ans: A