Write the vertex form of a parabola that satisfies the conditions given. Then write the equation in the form y=ax^2+bx+c .
Vertex (5,3) and a=2
vertex: y = 2(x-5)^2 + 3
y = 2x^2 - 20x + 53
Why did the parabola go to the comedy club?
Because it wanted to find its vertex form and crack some jokes!
The vertex form of a parabola with vertex (h, k) and a coefficient a is given by:
y = a(x - h)^2 + k
So using the given vertex (5,3) and a=2, the vertex form is:
y = 2(x - 5)^2 + 3
To simplify it further and write it in the form y = ax^2 + bx + c:
y = 2(x^2 - 10x + 25) + 3
y = 2x^2 - 20x + 50 + 3
y = 2x^2 - 20x + 53
So the equation of the parabola in the form y = ax^2 + bx + c is y = 2x^2 - 20x + 53.
To write the vertex form of a parabola, we use the formula:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Given that the vertex is (5, 3) and a = 2, we can substitute these values into the vertex form:
y = 2(x - 5)^2 + 3
Now, let's expand and simplify this equation to get it in the form y = ax^2 + bx + c:
y = 2(x^2 - 10x + 25) + 3
y = 2x^2 - 20x + 50 + 3
y = 2x^2 - 20x + 53
Therefore, the equation in the form y = ax^2 + bx + c for the given parabola is y = 2x^2 - 20x + 53.
To write the vertex form of a parabola, we use the formula y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
Given that the vertex of the parabola is (5,3) and the value of a is 2, we can substitute these values into the vertex form equation.
y = 2(x - 5)^2 + 3
To rewrite the equation in the form y = ax^2 + bx + c, we expand the equation using the distributive property.
y = 2(x^2 - 10x + 25) + 3
Now, distribute the 2 to each term inside the parentheses.
y = 2x^2 - 20x + 50 + 3
Finally, combine like terms to simplify the equation.
y = 2x^2 - 20x + 53
So, the equation of the parabola in the form y = ax^2 + bx + c is y = 2x^2 - 20x + 53.