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The quadratic (parabola) intercepts the x-axis when y = 0. So substitute y=0 into y = f(x). Then you can solve for the x-values by any number of ways: Factoring, completing the square, or Quadratic Formula. It may turn out that the values of x which satisfies y=0 are complex {have an imaginary component}, which will tell you that the parabola does not have an x-intercept.
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What determines if a quadratic function has no x-intercepts?
If the quadratic function is written as ax2 + bx + c, then it has no x-intercepts if the discriminant, (b2 - 4ac), is negative.
How aerospace engineers use the quadratic equation?
The quadratic equation is used to find the intercepts of a function (F(x)=x^(2*n), n being an even number) along its primary axis (typically the x axis). Many equations follow this form. The information given by the quadratic equation depends on what your function is pertaining to. If say you have a velocity vs time graph, when the function crosses the xaxis your particle has changed from a positive velocity to a negative velocity. This information can be useful to determine the accompanying behavior of your position. The quadratic equation is simply a tool to find intercepts of a function.
What does factoring a quadratic allow you to do?
Factoring a quadratic allows you to solve the x and y intercepts. The x-intercepts in the factored form are the inverse of the constants. The y-intercept is the product of the x-intercepts multipied together. Example: x²-10x-24 = (x+2)(x-12) +2 and -12 are the constants. So ur x-intercepts are (-2,0) (12,0). The y intercept is -24 because -2 X 12 = -24.
When does a quadratic curve have two x intercepts?
Two x intercepts- When the discriminant is greater than zeroOne x intercept- When the discriminant is equal to zeroNo x intercept- When the discriminant is less than zero
How do you make a graph of a quadratic function that has x-intercepts at 0 and 4?
That's not enough information to draw the graph. All you know is that it crosses the x-axis at those 2 points. You don't know whether it opens upward or downward, or how far the nose is above or below the x-axis. You need more information about the function before you can graph it. This is just another way of saying that there are an infinite number of different quadratic functions that all have those same x-intercepts.
