Quadratics

• The discriminant of a quadratic equation is the expression b^2 - 4ac, which determines the nature of the roots.
• To sketch a parabola, draw the axis of symmetry as a vertical line through the middle of the graph paper. Draw the vertex at the midpoint on this line. Plot points using the quadratic formula or table values. Join these points with a smooth curve.
• The vertex can be found by substituting the value of x into the quadratic formula to find y.
• The quadratic formula can be used to find the solutions of a quadratic equation: x = (-b ± √(b^2 - 4ac)) / (2a).
• If the discriminant is positive (b^2 > 4ac), there are two real solutions.
• If the discriminant is zero (b^2 = 4ac), there is one repeated root or a double root.
• If the discriminant is negative (b^2 < 4ac), there are no real solutions and the roots are complex conjugates.
• A quadratic function can be written in standard form (y = ax^2 + bx + c), factored form (y = a(x-h)(x-k)), or vertex form (y = a(x-h)^2+ k).
• To factor a quadratic expression, look for factors that multiply to give the first term and then use FOIL to check if it's correct.
• Quadratic functions have a parabola shape with a maximum or minimum point called the vertex.
• The y-intercept is found by setting x=0 and solving for y.
• The zeros of a quadratic function are also known as its roots or x-intercepts.
• The graph of a quadratic function opens upwards when a > 0 and downwards when a < 0.
• from standard to either factored or vertex