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Answer:
Option A) 1.6t+0.5
Step-by-step explanation:
Let
t ----> the number of trophies
we know that
To determine the total weight of the box, multiply the number of trophies by the weight of each trophy and add the weight of the empty box.
The linear equation that represent this problem is
<h2>Steps:</h2>
- Vertex Form: y = a(x - h)² + k with (h,k) as the vertex
So firstly, let's start with the vertex. Since this is in vertex form, we can find the vertex easily. Since 3 is in the h variable and -4 is in the k variable, <u>the vertex is (3,-4).</u>
Next, the axis of symmetry. Remember that the vertex's x-coordinate and the axis of symmetry are the same. In this case, since the vertex's x-coordinate is 3, this means that <u>the axis of symmetry is x = 3.</u>
Next, whether the vertex is a minimum or a maximum. To determine whether it's a minimum or a maximum, we look towards the a variable of the vertex form. If a is negative, then the parabola opens down and the vertex is a maximum. However, if a is positive, then the parabola opens up and the vertex is a minimum. In this case, a = 1 and since 1 is positive, <u>this makes the vertex a minimum.</u>
Next, to find the y-intercept plug 0 into the x-variable and solve:
<u>The y-intercept is (0,5).</u>
Next, to find the x-intercepts plug 0 into the y-variable to solve. Since it's a bit less straightforward than finding the y-intercept, I will walk through the steps:
Firstly, add 4 to both sides:
Next, square root both sides:
Next, add 3 to both sides:
Lastly, solve the left side twice: once with the plus sign, once with the minus sign:
<u>Your x-intercepts are (5,0) and (1,0).</u>
<h2>Answers:</h2>In short:
- Vertex: (3,-4)
- x-intercept(s): (5,0) and (1,0)
- y-intercept(s): (0,5)
- Axis of symmetry: x = 3
- Minimum or Maximum? Minimum.