I need help with parabolas

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

kelhaku Dec 17, 2023

#1**0 **

Combining the terms in the equation, we get:

y = -5x^2 - 6x + 10

To find the vertex of the parabola represented by this equation, we can rewrite it in vertex form:

y = a(x - h)^2 + k

where (h, k) is the vertex.

Here's how to find the vertex coordinates:

Identify the coefficient of the squared term: In this case, the coefficient of the squared term is -5. Since it's negative, the parabola opens downwards.

Find the x-coordinate of the vertex: The x-coordinate of the vertex is given by the formula:

h = -b / 2a

where b is the coefficient of the x term (-6 in this case).

h = -(-6) / (2 * -5) = 6/10 = 0.6

Find the y-coordinate of the vertex: Now that we know the x-coordinate of the vertex, we can plug it back into the equation to find the y-coordinate:

y = -5(0.6)^2 - 6(0.6) + 10

y = -1.8 - 3.6 + 10

y = 4.6

Therefore, the vertex of the parabola is (0.6, 4.6).

BuiIderBoi Dec 17, 2023