The vertex form is y = a(x – h)^2 + k.

The standard form is ax^2 + bx + c = 1.

The standard form is ax^2 + bx + c = 0, where a, b, and c are constants and x represents an unknown variable.

Ax^2 + Bx + C = 0, where A, B, and C can be variables.

Real roots are determined when discriminant < 0.

Calculate the discriminant using the formula b^2 - 4ac. If negative, there are real roots.

Calculate the discriminant using the formula b^2 - 4ac. If it is positive, there are two real roots; if zero, there is one real root; if negative, there are no real roots.

Use the formula c^2 - 4ab and check if positive.

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).

The quadratic formula is x = (b ± √(b^2 - 4ac)) / (2a).

The quadratic formula is x = (c ± √(b^2 + 4ac)) / (2a).

The quadratic formula is x = (b ± 2a) / (4ac).

Complex roots mean the roots are equal.

Complex roots occur when the discriminant (b^2 - 4ac) is negative, indicating that the solutions involve imaginary numbers.

Complex roots happen only when b = 0.

Complex roots are when b^2 - 4ac = 0.

Factoring transforms the equation to the form x^2 - a^2 = 0.

If a quadratic can be factored into (mx + n)(px + q) = 0, then the roots are found by setting each factor equal to zero and solving for x.

Use with complex roots only to simplify.

By transforming equation into a single linear equation.

'a' controls the y-intercept, 'b' changes the direction, 'c' is constant.

'a' scales the roots, 'b' is root difference, 'c' is angle.

In ax^2 + bx + c = 0, 'a' determines the parabola's direction and opening width, 'b' affects the position along the x-axis, and 'c' is the y-intercept.

'a', 'b', and 'c' all equally contribute to shape.

The vertex form is ax^2 + bx + c = y.

The vertex form is y = b(x – h)^2 + c.

The vertex form is y = a(x – h)^2 + k, where (h,k) is the vertex of the parabola.

The vertex form is y = a^2(x – h) + k.

Use the formula h = -b/(2a) to find the x-coordinate, and substitute it back into the equation to find the y-coordinate.

Set b = y and a = x to find the coordinates.

Plot the y-intercept to find the vertex.

Calculate the midpoint of the roots.

When (ax)^2 + bx + 1 = 0.

When it can be expressed in the form (ax)^2 + 2abx + b^2 = 0, representing (ax + b)^2.

When b^2 = 2a and c = 0.

When a > 0 and b = 0.

It reduces the quadratic to a simpler form of c(x + b).

It transforms a quadratic equation into a perfect square trinomial, making it easier to solve by taking the square root of both sides.

It finalizes the quadratic to be linearly solved.

It eliminates 'b' from the equation.

The sum is c/a, and the product is b/a.

For ax^2 + bx + c = 0, the sum of the roots is -b/a and the product is c/a.

The product is -b/a, and the sum is -c.

Both product and sum equal b^2 - 4ac.

A circle.

The graph of a quadratic function is called a parabola.

A hyperbola.

An ellipse.

Plot only the vertex and x-intercepts.

Identify the y-intercept only to plot.

Identify the vertex, axis of symmetry, x-intercepts, y-intercept, and plot these points to sketch the parabola.

Use only first and last coordinates.

'a' value does not affect the direction at all.

If 'a' is zero, it opens horizontally.

If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

'a' only affects the color of the graph.

A horizontal line dividing the graph in half.

The axis of symmetry is a vertical line x = -b/(2a) that divides the parabola into two symmetrical halves.

The line y = b that divides the parabola.

A diagonal line based on y-intercept.