More STAAR problems.
Administered May 2019
Read each question carefully. For a multiple-choice question, determine the
best answer to the question from the four answer choices provided. For a
griddable question, determine the best answer to the question.
46. The graph of quadratic function k is shown on the grid.
Which statements are best supported by the graph of k?
I. The x-intercept is located at (-3 0).
II. The coordinates of the y-intercept are (0, 9).
III. The axis of symmetry is x = -3.
F I and II only
G I and III only
H II and III only
J I, II, and III
Answer: J I, II, and III
The vertex is the x-intercept, and the axis of symmetry goes through the vertex at x = -3.
The y-intercept is (0, 9), which is a little difficult to see in the image. However, if you notice, the points go from (-3, 0), (-2, 1), (-1, 4), (0, 9). The y-coordinate increases +1, +3, +5, etc.
47. A college student has two different jobs. Her combined work schedules consist of no more than 48 hours in one week.
Which graph best represents the solution set for all possible combinations of x, the number of hours she worked at her first job, and y, the number of hours she worked at her second job,
in one week?
Answer: A
The more hours she works at one job, the fewer hours she can work at the other job. That is a declining slope from the y-intercept (Only works the second job) to the x-intercept (only works the first job).
And that line is the most she could work. She could work less, which is the area under the line.
48.Which function is equivalent to q(x) = 9x2 − 24x + 16?
F y = (9x - 4)(x - 4)
G y = (3x + 4)2
H y = (9x + 4)(x + 4)
J y = (3x - 4)2
Answer: J y = (3x - 4)2
You have to find those two middle terms and find which have a sum of -24x.
It should be obvious that G and H should be eliminated because the positive numbers cannot have a negative product.
Choice F has (9x)(-4) + (-4)(x) = -40x, which is incorrect.
Choice J has (3x)(-4) + (3x)(-4) = -24x, which is what we are looking for.
49. Which graph best represents this system of equations and its solution?
3x + 15y = −6
Answer: B
One option is to find the x-intercept and y-intercept of each line.
8x - 4y = -16
8x = -16 and -4y = -16
x = -2 and y = 4
(-2, 0) and (0, 4)
Only Choice B has these two points.
3x + 15y = -6
3x = -6 and 15y = -6
x = -2 and y = -6/15
(-2, 0) and (0, -6/15)
Choice B has these points. (You can estimate the y-intercept)
50. What are the domain and range of g(x) = -1/4(x - 17)2 + 61?
F Domain: All real numbers; Range g(x) < 61
G Domain: x < 17; Range g(x) < 61
H Domain: All real numbers; Range g(x) < 17
I Domain: x > 17; Range g(x) < 17
Answer: A y = 1.2x - 6
All values of x are valid input for this function. There are no value for which the function would not be defined. Choices G and J are eliminated.
The function is a quadratic. It's a parabola with a vertex at (17, 61). The leading coefficient is negative, so the vertex is a maximum. All values of the range must be below the vertex, so g(x) < 61, which is Choice F.
Also notice that in Choice H, the range is given in terms of x, which makes no sense.
More to come. Comments and questions welcome.
More STAAR problems.
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