How Do You Graph a Quadratic Equation with No Solution?

x=-b/(2a) is the formula for the axis of symmetry
2²-4(2)+5=4-8+5=1
Let's create a table to help us graph!
That yellow dotted line is the axis of symmetry, and it cuts our parabola in half!
The parabola doesn't cross the x-axis, which means there are no zeros for this polynomial

1. This is the formula for the axis of symmetry
1. Now we can plug these into the formula of the axis of symmetry:
2. It's x=-b/(2a)
1. -(-4)=4
2. 2(1)=2
3. 4/2=2
1. The vertex is either the maximum or minimum value of the parabola
1. Our axis of symmetry is x=2, so the vertex must have an x value of 2
1. Since 2 is the x-value of our vertex, we can find the y-value by plugging 2 in for x in our original equation
2. We get 2²-4(2)+5 after pluggin in
3. That reduces to 4-8+5, which is equal to 1
1. We're plugging 0, 1, 2, 3, and 4 into the polynomial x²-4x+5
2. Simplifying we get the points:
3. (0,5)
4. (1,2)
5. (2,1)
6. (3,2)
7. (4,5)
1. Remember, our axis of symmetry was the vertical line x=2
1. The zeros of a function are where the graph crosses the x-axis
2. They are the points where y=0
3. These points will be the solutions to our equation
1. Zeros are the points where y=0
1. Since we can never make the left hand side of our equation equal 0, there are no solutions to this equation

Solve x2 - 4x + 5 = 0 by graphing.