Find the the vertex and axis of symmetry using any method Do

Find the the vertex and axis of symmetry using any method. Do not graph. (Simplify the coordinates of the vertex completely.) y = 5x^2 + 30x + 46 vertex (x, y) = () axis of symmetry

Solution

We have y = 5x² + 30x + 46.This is the standard form of the equation of a parabola. We know that when the equation of a parabola is y = ax² + bx + c, the axis of symmetry is the line x = -b/2a. Here, a = 5 and b = 30, so that the axis of symmetry is the line x = - 30/2*5 = -30/10 or x = - 3.

On converting the given standard form of the equation to vertex form, we have y = 5( x² + 6x + 9)+1=5(x + 3)² +1. We know that when the equation of a parabola is y = (x -h)² + k, the vertex of the parabola is (h , k). Here, h = -3 and k = 1. Therefore, the vertex of the parabola is at ( -3, 1).

vertex ( x,y) = ( -3, 1); axis of symmetry x = - 3

We know that the vertex form of the equation of a parabola is y = a( x - h)² + k. The vertex of this parabola is (h, k) and if a> 0, the parabola opens upwards. Here,