Question

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. Identity the equation for the axis of symmetry, write the solutions and the coordinates of the vertex as ordered pairs. Show as much work as possible for full credit. All work should be done by hand.

Answer 1

See explanation

Explanation:

1. Factor the function
`f(x)=-2x^2+16x-30:`

`f(x)=-2x^2+16x-30=-2x^2+6x+10x-30=-2x(x-3)+10(x-3)=-2(x-3)(x-5).`

2. The zeros (or the solutions of the equation f(x)=0) are x=3 and x=5. So? points (3,0) and (5,0) are the points on the graph that are the solutions of the equation.

3. Find the vertex:

`x_v=-(b)/(2a)=-(16)/(2\cdot (-2))=4,\\ \\y_v=-2\cdot 4^2+16\cdot 4-30=-32+64-30=2.`

Thus, the coordinates of the vertex are (4,2) and the axis of symmetry is the vertical line that passes trough the vertex: x=4.