Hi,
When I have a quadratic equation, ax^2 + bx + c, can I find the y-intercept by looking at the last digit like I can when I have a linear equation?
For example, 3x^2 + 10x + 2, the y-intercept is (0, 2)
To check, if I make x = 0, 3(0)^2 + 10(0) + 3 = 3, so my y-intercept is (0, 3), so it checks out, but does this always work for quadratic equations?
Thank you
yes, that works for any polynomial in standard form (descending powers of the variable).
Don't be surprised if it happens to come out zero, though, as with
y = 2x^2 - 5x
sure ... making x=0 puts you on the y-axis ... so that's the y-intercept
So I can always just look at the last number of the equation, though, to see what the y-intercept is??
When you have a quadratic equation in the form ax^2 + bx + c, finding the y-intercept is slightly more complex than with a linear equation. The y-intercept represents the point where the graph intersects the y-axis, and for a quadratic equation, it is the value of y when x equals zero.
To find the y-intercept of a quadratic equation, you substitute x = 0 into the equation and solve for y. So, in your example equation, 3x^2 + 10x + 2, if you let x = 0, the equation becomes 3(0)^2 + 10(0) + 2 = 2. Therefore, the y-intercept is (0, 2).
It is important to note that finding the y-intercept by simply looking at the last term c is only a coincidence in some cases. If the constant term c in the quadratic equation is equal to the y-intercept, then this shortcut works. However, this method is not always reliable, especially when there is a non-zero coefficient for x^2 or x.
To find the y-intercept, it's generally better to use the substitution method described above.