Lesson 112: Graphing and Solving Systems of Linear and Quadratic Equations — Practice Questions

1. 1. A right triangle has legs with lengths of 8 cm and 15 cm. What is the length of the hypotenuse in cm? The answer is ___.

2. 2. When solving a system of equations by graphing, what does an intersection point of the two graphs represent?

   • A. The y-intercept of one equation
   • B. A solution that satisfies both equations
   • C. The vertex of a parabola
   • D. The slope of a line

3. 3. Which ordered pair is a solution to the system of equations given by $y = x^2$ and $y = x + 6$?

   • A. (2, 4)
   • B. (3, 9)
   • C. (1, 7)
   • D. (-1, 5)

4. 4. A 100-foot kite string is pulled tight, and the kite is directly above a tree. If the height of the kite is 80 feet, what is the horizontal distance from the person holding the string to the tree? The distance is ___ feet.

5. 5. The graphs of $y = x^2 - 3$ and $y = 1$ are drawn on the same coordinate plane. How many solutions does this system of equations have?

   • A. 0
   • B. 1
   • C. 2
   • D. 3

6. 6. To solve the system of equations $y = x^2 + 5x$ and $y = 2x + 10$, you must first form a quadratic equation set to zero. What is this equation? ___

7. 7. When solving a system like $y = x^2 + 2x$ and $y = 4x - 1$, what is the primary goal of setting $x^2 + 2x = 4x - 1$?

   • A. To find the y-intercept of the parabola.
   • B. To eliminate the variable $y$ and create a single equation with only $x$.
   • C. To find the vertex of the quadratic equation.
   • D. To check if the line and the parabola are parallel.

8. 8. The system of equations $y = x^2 - 4x + 5$ and $y = x + 1$ has two intersection points. One point is $(1, 2)$. What is the other intersection point? ___

9. 9. Use the distributive property to simplify the expression $8(2x - 3)$. The simplified expression is ___.

10. 10. A student incorrectly simplifies the expression $7(x + 4)$ to $7x + 4$. What is the specific error the student made?

    • A. The student added instead of multiplying.
    • B. The student should have only multiplied the 7 and the 4.
    • C. The student distributed the 7 to the first term but not to the second term.
    • D. The student should have simplified the terms inside the parentheses first.