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.
26.The graph of linear function f passes through the point (1, −9) and has a slope of -3.
What is the zero of f?
F 2
G 4
H -6
J -2
Answer: J -2
I included the blank graph because the visual makes the problem easier to solve. Make a point at (1, -9). If the slope is -3, it's going down 3 and to the right 1. That means it also goes up 3 and 1 to the left. If you move that way, you get to (0, -6). Keep going and you get to the x-axis at (-2, 0).
If you don't want to use the graph, you could solve the equation
0 - (-9) = -3(x - 1)
9 = -3x + 3
6 = -3x
-2 = x
27. What is the value of the y-intercept of the graph of h(x) = 29(5.2)x?
Record your answer and fill in the bubbles on your answer document.
Answer: 29
At the y-intercept, x = 0.
h(0) = 29(5.2)0 = 29(1) = 29
28. The graph of a quadratic function is shown on the grid.
Which function is best represented by this graph?
F h(x) = x2 - 3x - 9
G h(x) = x2 + 3x - 9
H h(x) = x2 - 6x
J h(x) = x2 + 6x
Answer: H h(x) = x2 - 6x
As always, you could put the functions into your graphing calculator and check. However, we can reason these out.
First of all, for a parabola that opens upward, when the middle term, the x term, of a quadratic function is negative, the parabola is shifted to the right. If it is positive, it gets shifted to the left. So we can eliminate G and J.
Second, the constant is the y intercept, which in the graph is the origin, or 0. That eliminates choice F. J is the answer.
If you needed a third reason, the Axis of Symmetry is x = -b / (2a). The graph shows the Axis (the vertical line going through the vertex) at x = 3. This eliminates F and G immediately, and J after you do a quick mental check on the signs.
29. Which expression is equivalent to 24x2 - 22x + 5?
A (12x + 5)(2x + 1)
B (8x - 5)(3x - 1)
C (12x - 5)(2x - 1)
D (8x + 5)(3x + 1)
Answer: C (12x - 5)(2x - 1)
There are choices that you can "FOIL" (box method, distribute, etc) instead of trying to factor this mess.
Look at the signs. You have -22x and + 5. The only way to get that is if there are minus signs in both of the binomials. This eliminates A and D.
A quick check shows that both B and C will produce 24 and +5, so you have to check the two middle terms, the Outer and Inner.
(8)(-1) + (-5)(3) = -23
(12)(-1) + (-5)(2) = -22. Choice C is the answer.
30. A system of equations is graphed on the grid.
Which system of equations does the graph represent?
F y = -x - 4 ; y = 2x - 2
G y = -x + 4 ; y = 2x - 4
H y = -x - 4 ; y = 2x - 2
J y = -x + 4 ; y = 2x - 4
Answer: J y = -x + 4 ; y = 2x - 4
A curious problem, given that the y-intercept are obviously 4 and -4, Choices F and H can be immediately eliminated.
The line that's increasing gets the + 4, and it has to have a positive slope. That makes J the correct answer. Likewise, the decreasing line gets the - 4, which is also J.
You don't have to calculate a thing for this problem.
I would've thought that they would have you calculate at least one slope, just to be sure. However, that isn't necessary at all.
More to come. Comments and questions welcome.
More STAAR problems.
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