How many x or y intercepts can a quadratic function have?
A) 0-2 x-intercepts and 0-1 y-intercept
B) 0-2 x-intercepts and 1 y-intercept
C) 2 x-intercepts and 1 y-intercept
D) 1-2 x-intercepts and 0-1 y-intercept
I think the answer is D.
nope. Think of y=x^2+1
Is it C?
No. consider y = (x-1)^2
Try sketching a parabola in various positions. You only have two choices left ...
You are correct, the answer is D) 1-2 x-intercepts and 0-1 y-intercept.
To determine the number of x-intercepts a quadratic function can have, we need to consider the discriminant, which is part of the quadratic formula. The discriminant is given by the expression b^2 - 4ac, where a, b, and c are coefficients of the quadratic equation in the form ax^2 + bx + c.
If the discriminant is positive, there are two distinct x-intercepts.
If the discriminant is zero, there is one x-intercept (known as a double root).
If the discriminant is negative, there are no real x-intercepts, only complex solutions.
For the y-intercept, we need to evaluate the value of the function when x is zero, as the y-intercept is the point where the graph intersects the y-axis.
In the case of a quadratic function, there can be 0-2 x-intercepts and 0-1 y-intercepts. So, option D) 1-2 x-intercepts and 0-1 y-intercept is the correct answer.