a square is a figure with two pairs of parallel sides and four write angles. is the statement a good definition? if not find a c
2 answers:
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Answer:
Step-by-step explanation:
If you plot the vertex and the point, you see that the point is above the vertex. Therefore, this is a positive parabola with the work form of
We have values for x, y, h, and k. Let's write the equation of the parabola, put it into function notation, then find another x value at which to evaluate it.
and
and
8 = 9a - 1 and
9 = 9a so
a = 1. The equation of the parabola in function notation is
Since the vertex is at (3, -1) it would make sense to evaluate the function at x values close to the vertex. Let's evaluate the function at an x value of 4:
and
and
f(4) = 0. That means that another point on this parabola will be (4, 0).
<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.