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X and Y Intercepts of Quadratic Function



X-intercept is the points in cartesian coordinate where a quadratic curve intersects with the x-axis. A quadratic function may either intersect with x-axis in 2 points, in 1 points or don't intersect x-axis at all depending on the value of its Discriminant. If the Descriminant value is positive, the quadratic curve is going to intersect with x-axis in 2 points. If the Discriminant value is exactly zero, the quadratic curve is going to intersect with x-axis in two points. If the Discriminant value is negative, the quadratic curve is not going to intersect with x-axis in real coordinate system.


Y-intercept in other hand, is a point in cartesian coordinate where a quadratic curve intersects with the y-axis. All quadratic function with real constant is going to intersect with y-axis in exactly one point.


All you have to do is to check any check boxes with captions x-intercept and y-intercept ( see the picture above ). Then click as HTML to tell Orimath Quadratic Solver to solve the problem for you and tell you the steps required to get the answer.





Answer by Orimath Quadratic Solver :
Question Number 1 :
For this function y(x) = x2 + 5x + 4 , answer the following questions :

Answer Number 1 :
The equation x2 + 5x + 4 = 0 is already in ax2+bx+c=0 form.
Then we can imply that the value of a = 1, b = 5, c = 4.

The points where y = x2 + 5x + 4 intersect with x-axis,
Is where the value of y = 0
A way to find value of x and y that match both equations is by subtituting y with 0
Then we have to solve the equation : x2 + 5x + 4 = 0
To solve the equation we will use completing the square
x2 + 5x + 4 = 0 ,divide both side with 1
By doing so we get x2 + 5x + 4 = 0 ,
Which means that the coefficient of x is 5
We have to use the fact that ( x + q )2 = x2 + 2qx + q2 , and assume that q = 5/2 = 2.5
By using that fact we turn the equation into x2 + 5x + 6.25 - 2.25 = 0
Which can be turned into ( x + 2.5 )2 - 2.25 = 0
Which can be turned into (( x + 2.5 ) - 1.5 ) * (( x + 2.5 ) + 1.5 ) = 0
By opening the brackets we will get ( x + 2.5 - 1.5 ) ( x + 2.5 + 1.5 ) = 0
Just add up the constants in each brackets, and we get ( x + 1 ) * ( x + 4 ) = 0
So the function have 2 x-intercept in ( x , y ) = ( -1 , 0 ) and ( x , y ) = ( -4 , 0 )
For the curve y = x2 + 5x + 4 to intersect with y-axis,
We have to remember that y-axis itself is a line with equation x = 0
So the next thing we have to do is subtituting x with 0 in y = x2 + 5x + 4
So we get y = 1 (0)2 + 5 (0) + 4
Which make y = 4
So the function have y-intercept in ( x , y ) = ( 0 , 4 )




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