How are the real solutions of a quadratic equation related to the graph of the quadratic function?
Solution:
The graph of a quadratic is in the form of a parabola
The number of times the graph cuts the x-axis is equal to the number of solutions of the quadratic equation and the x coordinate of that point becomes one of the solutions of the equation
If the graph does not cut the x-axis at all the equation is said to have imaginary or unreal roots.
If the graph cuts the x-axis at two points then the equation has two distinct real roots which are equal to the x coordinate of those two points.
If the graph just touches the x axis at 1 point then it is said to have two equal and real roots such that the roots = x coordinate of that point.
For example:
Consider a quadratic equation y = x2 - 5x + 6
Let us take y = 0
So we get
x2 - 5x + 6 = 0
x2 - 2x - 3x + 6 = 0
Taking out the common terms
x(x - 2) - 3(x - 2) = 0
(x - 2)(x - 3) = 0
So we get
x = 3 and x = 2
So if y = 0, x = 3 and x = 2.
Therefore, the relationship between the real solutions and the graph of the quadratic function are mentioned above.
How are the real solutions of a quadratic equation related to the graph of the quadratic function?
Summary:
The relationship between the real solutions and the graph of the quadratic function are mentioned above.
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