Select the correct answer. This graph represents a quadratic function. What is the value of a in this function’s equation? A)-1
B)2 C)1 D)-2
2 answers:
Answer:
Step-by-step explanation:
We will use the work form of a quadratic to determine what a is...in fact we will write the equation for the whole thing in the process, because it's part of solving for a.
y = ±|a|(x - h)² + k
where x and y are from a coordinate point on the graph, h and k are the coordinates of the vertex, the absolute value of a indicates how steep or flat the graph is compared to the parent graph, and the ± is because a positive parabola opens up and a negative one opens upside down.
The vertex is (0, 9) and the coordinate point I chose to use is (3, 0). Filling those in and solving for a:
0 = ±|a|(3 - 0)² + 9 and
0 = ±|a|(3)² + 9 and
-9 = ±|a|9 and
-1 = ±|a| so a = 1. Because this is an upside down parabola the negative is out front, but a is independent of it. The correct choice is C. The quadratic function is
or in more detailed form:
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Answer:
- all right angles are congruent.
- opposite sides of a parallelogram are congruent
- SAS congruence postulate
- corresponding parts of congruent triangles are congruent
Step-by-step explanation:
Given : Parallelogram JKLM is a rectangle and by the definition of rectangle, are right angles,
Since all interior angles of rectangle are right angle.
then , because all right angles are congruent.
Also, opposite sides of a parallelogram are congruent.
and by the reflexive property of congruence.
Now, by the SAS congruence postulate,
,
Since corresponding parts of congruent triangles are congruent, ∴
- The SAS postulate says that if two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle then the two triangles are congruent.