How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y = 2x^2 - 4x -3?

1 Answer

Axis of symmetrycolor(blue)(" "x=1)
Minimum value of the function color(blue)(=-5)
See the explanation for the graph

Explanation:

The solution:

To find the Axis of symmetry you need to solve for the Vertex (h, k)

Formula for the vertex:
h=(-b)/(2a) and k=c-b^2/(4a)

From the given y=2x^2-4x-3
a=2 and b=-4 and c=-3

h=(-b)/(2a)=(-(-4))/(2(2))=1
k=c-b^2/(4a)=-3-(-4)^2/(4(2))=-5

Axis of symmetry:

x=h

color(blue)(x=1)

Since a is positive, the function has a Minimum value and does not have a Maximum.

Minimum value color(blue)(=k=-5)

The graph of y=2x^2-4x-3
Desmos.comDesmos.com

To draw the graph of y=2x^2-4x-3, use the vertex (h, k)=(1, -5) and the intercepts.

When x=0,
y=2x^2-4x-3
y=2(0)^2-4(0)-3=-3" "means there is a point at (0, -3)

and when y=0,
y=2x^2-4x-3
0=2x^2-4x-3

x=(-b+-sqrt(b^2-4ac))/(2a)=(-(-4)+-sqrt((-4)^2-4(2)(-3)))/(2(2))

x=(+4+-sqrt(16+24))/(4)

x=(+4+-sqrt(40))/(4)

x=(+4+-2sqrt(10))/(4)

x_1=1+1/2sqrt(10)

x_2=1-1/2sqrt(10)

We have two points at (1+1/2sqrt(10), 0) and (1-1/2sqrt(10), 0)

God bless...I hope the explanation is useful.