Solving Quadratic Equations

Front

What are the solutions, roots, x-intercepts, and zeros of a quadratic equation?

Back

They are all the same thing; they refer to the values of x where the quadratic equation equals zero.

Front

How do you find the solutions of a quadratic equation from its graph?

Back

The solutions are the x-coordinates where the graph intersects the x-axis.

Front

What is the significance of the x-intercepts in a quadratic function?

Back

The x-intercepts represent the solutions of the quadratic equation, indicating where the function equals zero.

Front

What does it mean if a parabola has two zeros?

Back

It means the quadratic equation has two distinct real solutions.

Front

What does it indicate if a quadratic equation has no real solutions?

Back

It indicates that the parabola does not intersect the x-axis, resulting in zero x-intercepts.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How can you determine the number of solutions of a quadratic equation using the discriminant?

Back

The discriminant (b^2 - 4ac) indicates the number of solutions: if it's positive, there are 2 solutions; if zero, 1 solution; if negative, no real solutions.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.