a. Write an equation compared to the equation of the standard parabola that satisfies the description of each parabola.
1. A parabola whose vertex is (0, -3)
2. A parabola whose vertex is (5, 1)
3. A parabola that opens down and is compressed vertically by a factor of 0.4
4. A parabola that has its vertex at (3, 5) and opens down.
5. A parabola that has its vertex at (-8, 6) and opens up, but is stretched vertically by a factor of 3, compared with the standard parabola.
#1: y = x^2-3
#2: y = (x-5)^2+1
#3: y = -0.4x^2
#4: y = -(x-3)^2-5
you get the idea... I hope
Thank you Anonymous.
To Nameless:
In case you have not yet verified, the fourth one should read
y = -(x-3)^2 + 5
in order to have the vertex at (3,5).
Suggest you post your attempt for the fifth.
To find the equation of a parabola, we need to use the general equation of a parabola and the given information about the vertex and other characteristics.
The general equation of a parabola is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
1. For a parabola with a vertex at (0, -3), the equation will be y = a(x - 0)^2 - 3, which simplifies to y = ax^2 - 3.
2. For a parabola with a vertex at (5, 1), the equation will be y = a(x - 5)^2 + 1.
3. To describe a parabola that opens downward and is vertically compressed by a factor of 0.4, we will modify the equation. The equation will be y = a(x - h)^2 + k, but since it opens downward and is compressed vertically, the value of 'a' will be negative and less than 1. Let's say a = -0.4, then the equation becomes y = -0.4(x - h)^2 + k.
4. For a parabola with a vertex at (3, 5) and opens downward, the equation will be y = a(x - 3)^2 + 5. Since it opens downward, 'a' will be negative.
5. To describe a parabola that opens upward, has a vertex at (-8, 6), and is vertically stretched by a factor of 3, we will modify the equation. The equation will be y = a(x - h)^2 + k, but since it opens upward and is stretched vertically, the value of 'a' will be positive and greater than 1. Let's say a = 3, then the equation becomes y = 3(x - (-8))^2 + 6.
These equations represent the parabolas satisfying the given descriptions. Please note that the values of 'a', 'h', and 'k' may vary depending on the specific characteristics of each parabola.