1.
Which best describes the graph of a quadratic function?
Correct Answer
B. A u-shape.
Explanation
The graph of a quadratic function is best described as a u-shape because it forms a curve that opens either upward or downward. This curve is symmetric and smooth, resembling the shape of the letter "U". The u-shape is characteristic of quadratic functions, which are second-degree polynomial functions. It is important to note that a quadratic function can open upward or downward depending on the coefficient of the quadratic term.
2.
How do you change the direction of the graph of a quadratic function?
Correct Answer
B. Change the sign in front of x^2.
Explanation
To change the direction of the graph of a quadratic function, you need to change the sign in front of x^2. This is because the coefficient of x^2 determines whether the parabola opens upwards or downwards. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. By changing the sign in front of x^2, you are essentially changing the coefficient and therefore changing the direction of the graph.
3.
I want to move the graph ________ the y-axis, so I am going to add 7.
Correct Answer
up
Explanation
The correct answer is "up" because the statement mentions moving the graph along the y-axis, and adding a positive value to the y-coordinate will shift the graph upwards.
4.
Subtracting 7 from y=x^{2}+2x will move the graph how?
Correct Answer
D. Down 7.
Explanation
Subtracting 7 from the equation y = x^2 + 2x will result in y = x^2 + 2x - 7. This means that the entire graph will shift downward by 7 units. The vertex of the parabola will also shift downward, resulting in a new minimum point that is 7 units lower than the original minimum point. Therefore, the correct answer is "Down 7."
5.
To make the graph y=x^{2}+4x+7 just grow faster I would do the following:
Correct Answer
C. Multiply the number in front of x^2 by a number bigger that 1.
Explanation
By multiplying the number in front of x^2 by a number bigger than 1, the graph of the equation y=x^2+4x+7 will become steeper and grow faster. This is because the coefficient of x^2 determines the rate at which the graph increases or decreases. When this coefficient is multiplied by a number greater than 1, it amplifies the effect of the x^2 term, causing the graph to become steeper.
6.
To make y=6x^{2}+4 just grow slower I would...
Correct Answer
E. Multiply the number in front of x^2 by a number in between 0 and 1.
Explanation
To make the equation y=6x^2+4 grow slower, we need to decrease the coefficient in front of x^2. Multiplying it by a number between 0 and 1 would achieve this. This is because multiplying a number by a value between 0 and 1 reduces its magnitude, resulting in a slower growth rate.
7.
The graph of y=x^{2} has a/an __________________ point.
Correct Answer
minimum
min
Explanation
The graph of y=x^2 has a minimum point. This is because the graph of a quadratic function in the form y=ax^2+bx+c opens upward when the coefficient "a" is positive, like in this case. The minimum point is the lowest point on the graph, where the function reaches its minimum value. In this case, the minimum point occurs at the vertex of the parabola, which is at the origin (0,0). Therefore, the correct answer is "minimum" or "min".
8.
The graph of y = - 7x^{2 }+ 7x + 4 has a/an __________________ point.
Correct Answer
maximum
max
Explanation
The graph of the given equation is a downward-opening parabola. Since the coefficient of the x^2 term is negative, the parabola opens downwards. The term "maximum" refers to the highest point on the graph. Therefore, the correct answer is "maximum" or "max".
9.
Will the graph of a quadratic ever cover both all of the positive and negative y-values?
Correct Answer
B. No.
Explanation
It will either go up forever and miss some negative y-values, or go down forever and miss some positive y-values.
10.
Quadratic functions have a line of symmetry.
Correct Answer
A. True.
Explanation
Quadratic functions have a line of symmetry because the graph of a quadratic function is a parabola, and a parabola is symmetric about its line of symmetry. This means that if you draw a vertical line through the vertex of the parabola, the two sides of the parabola will be mirror images of each other. Therefore, the statement is true.