Click here to learn more about Quadratic Equations. The graph of an equation in the form y = ax^2 + bx + c is a parabola.
Most videos show how to determine if the parabola goes up or down, the equation of the axis of symmetry, the vertex point. Some discuss how to also find the x-intercepts (if any) and the y-intercept, and how to graph the parabola(s).
Par1: Parabolas Part 1: Graph f(x) = x^2, f(x) = x^2 - 4, f(x) = x^2 + 2, f(x) = x^2 - 6
Par2: Parabolas Part 2: Coefficient of x^2 is negative; Graph f(x) = -x^2, Graph f(x) = -x^2 + 7, Graph f(x) = -x^2 + 4
Par3: Parabolas Part 3: Graph f(x) = x^2, f(x) = (x - 1)^2, f(x) = (x +2)^2, f(x) = (x + 1)^2,
Par4: Parabolas Part 4: Graph f(x) = -(x + 1)^2, f(x) = (x - 2)^2 - 4, f(x) = -(x - 3)^2 + 6
Par5: Parabolas Part 5: Graph f(x) = x^2, f(x) = (1/2)x^2, f(x) = -2x^2, f(x) = (-2/3)x^2, f(x) = (1/4)x^2
Par6: Parabolas Part 6: Graph f(x) = (1/2)(x + 1)^2 - 3, f(x) = -2(x + 3)^2 + 8
Par7: Completing the Square to get a parabola in standard form: This video shows how to get a formula for the equation of the line that is the axis of symmetry, and how to find the vertex point by completing the square on a the equation of a parabola in the form y = ax^2 + bx + c. The formula is then used to find the vertex point for y = x^2 - 4x + 5.
Below are 5 videos showing how to find the x and y intercepts of a parabola, and how to round if the x-intercepts are irrational.
Parabola x and y intercepts 1: https://youtu.be/TPbsTUNnFKQ
Parabola x and y intercepts 2: https://youtu.be/lfPJ-A6woNo
Parabola x and y intercepts 3: https://youtu.be/ayEe_IA5rfM
Parabola x and y intercepts 4: https://youtu.be/LUmyENCT_2A
Parabola x and y intercepts 5: https://youtu.be/XFoFkPqGI7Q
These videos show how you can use a formula to find the vertex point, and then graph.
Par8: Parabolas Part 7: Graph f(x) = -3x^2 + 6x + 4
Par9: Parabolas Part 8: Graph f(x) = (1/2)x^2 + 2x + 6
Bummer: This next one doesn't have audio after 2:50. Sorry!!!! Hopefully you can follow along by watching.
Par10: Parabolas Part 9: Graph f(x) = -2x^2 + 6x
Par11: Parabolas Part 10: Given the equation of a parabola that is a function in different forms, several examples are provided and we state if the parabola goes up or down, the equation of the axis of symmetry, the vertex point, and y-intercept.
Par12: Find max height of ball: http://youtu.be/3PfiCtfmJA8
This video uses the vertex point of a parabola to find the maximum height of ball thrown in the air given its initial speed.
Max and Min Problems--uses the idea of the vertex of a parabola to find a minimum or maximum value
Click Here to see applications solving equations in the form of quadratics.