Algebraically, determine the vertex form of a quadratic relation, if the vertex is at (-1, 2) and the point (1, -10) is on the parabola. Show all of your steps.
I know that the formula is y=a(x-h)suared+ k but how do i apply these numbers to this formula?
Thank you!
given the vertex, you know that
y-2 = a(x+1)^2
Since (1,-10) is on the graph,
-10-2 = a(1+1)^2
-12 = 4a
a = -3
y-2 = 3(x+1)^2
To find the vertex form of the quadratic relation, we need to use the formula y = a(x - h)^2 + k and substitute the coordinates of the vertex (-1, 2) into the equation.
Step 1: Substitute the x-coordinate of the vertex (-1) for h and the y-coordinate (2) for k:
y = a(x - (-1))^2 + 2
Step 2: Simplify the equation:
y = a(x + 1)^2 + 2
Now, we use the fact that the point (1, -10) is on the parabola to determine the value of a.
Step 3: Substitute the x-coordinate of the point (1) for x and the y-coordinate (-10) for y in the equation:
-10 = a(1 + 1)^2 + 2
Step 4: Simplify the equation:
-10 = a(2)^2 + 2
Step 5: Simplify further:
-10 = 4a + 2
Step 6: Subtract 2 from both sides:
-12 = 4a
Step 7: Divide by 4 on both sides to solve for a:
a = -3
Now, substitute the found value of a into the equation to obtain the vertex form of the quadratic relation.
Step 8: Substitute a = -3 into the equation from Step 2:
y = -3(x + 1)^2 + 2
Hence, the vertex form of the quadratic relation with the given vertex (-1, 2) and point (1, -10) is y = -3(x + 1)^2 + 2.
To find the vertex form of a quadratic relation, you need to use the information given about the vertex and another point on the parabola. In this case, the vertex is (-1, 2) and the point (1, -10) is on the parabola.
Step 1: Find the value of "a"
The general form of a quadratic equation, y = ax^2 + bx + c, can be rewritten in vertex form as y = a(x - h)^2 + k. To find the value of "a," we can substitute the coordinates of one of the given points into the equation.
Using the point (1, -10), we have:
-10 = a(1 - (-1))^2 + 2
Simplifying this equation, we get:
-10 = 4a + 2
Subtracting 2 from both sides, we have:
-12 = 4a
Dividing by 4, we find:
a = -3
Step 2: Substitute the values into the vertex form equation
Now that we have the value of "a," we can substitute it, along with the vertex coordinates, into the vertex form equation: y = a(x - h)^2 + k.
Substituting a = -3, h = -1, and k = 2, we get:
y = -3(x - (-1))^2 + 2
Simplifying further, we have:
y = -3(x + 1)^2 + 2
So, the vertex form of the quadratic relation is y = -3(x + 1)^2 + 2.
Remember, the steps involved in finding the vertex form of a quadratic equation are:
1. Find the value of "a" by plugging in the coordinates of one of the given points.
2. Substitute the values of "a," "h" (x-coordinate of the vertex), and "k" (y-coordinate of the vertex) into the vertex form equation y = a(x - h)^2 + k.