Quadratic Equations Review

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: if D > 0, there are 2 real solutions; if D = 0, there is 1 real solution; if D < 0, there are no real solutions.

Front

Solve: 2x² + 6x = 7

Back

x = -1, -3.5

Front

Solve: 9x² - 16 = 0

Back

x = ± 4/3

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).

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 images, given by the equation x = -b/(2a).

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, depending on the direction it opens (upward or downward).

Front

If the discriminant is positive, how many real solutions does the quadratic have?

Back

2 Real Solutions.

Front

If the discriminant is zero, how many real solutions does the quadratic have?

Back

1 Real Solution.