x-intercepts of a parabola
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to find the x-intercepts of a parabola, which are the points where the parabola crosses the x-axis. Students set y = 0 in the quadratic equation and solve for x using factoring, the quadratic formula, or other methods.
Key Concepts
Property To find the $x$ intercepts of the graph of.
$$y = ax^2 + bx + c$$.
we set $y = 0$ and solve the equation.
Common Questions
What are the x-intercepts of a parabola?
The x-intercepts are the points where the parabola crosses the x-axis, meaning y = 0. They are also called the roots or zeros of the quadratic equation.
How do you find the x-intercepts of a parabola?
Set y = 0 and solve the quadratic equation ax^2 + bx + c = 0 by factoring, using the quadratic formula, or completing the square.
Can a parabola have no x-intercepts?
Yes. If the discriminant (b^2 - 4ac) is negative, the parabola does not cross the x-axis and has no real x-intercepts.
Can a parabola have exactly one x-intercept?
Yes. When the discriminant equals zero, the parabola just touches the x-axis at exactly one point, called the vertex.
Where are x-intercepts of a parabola taught?
X-intercepts of a parabola are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.