Question

If \[D > 0\], how does the parabola \[y = ax^{2} + bx + c\] behave with respect to the x-axis, and how many x-intercepts does it have?

Options

• The parabola touches the x-axis at one point; 1 x-intercept

• The parabola lies entirely above the x-axis; 1 x-intercept

• The parabola does not meet the x-axis; 0 x-intercepts

• The parabola cuts the x-axis at two points; 2 x-intercepts

Answer 1

When \[D > 0\], the parabola cuts the x-axis at two points, giving 2 x-intercepts. This corresponds to the two distinct real roots obtained from \[\pm \sqrt{b^{2} - 4ac}\] in the quadratic formula.