Solve by graphing quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by setting y = 0.

Front

How do you find the x-intercepts of the equation 2(x + 5)(x + 1) = 0?

Back

Set each factor to zero: x + 5 = 0 (x = -5) and x + 1 = 0 (x = -1). The x-intercepts are x = -5 and x = -1.

Front

What does it mean if a quadratic graph has a minimum?

Back

A minimum means the vertex of the parabola is the lowest point on the graph, indicating the function opens upwards.

Front

How do you solve the equation (x - 5)(x - 1) = 0 for x?

Back

Set each factor to zero: x - 5 = 0 (x = 5) and x - 1 = 0 (x = 1). The solutions are x = 5 and x = 1.

Front

What is the vertex form of a quadratic equation?

Back

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

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 x = -b/(2a).

Front

How can you determine if a quadratic opens upwards or downwards?

Back

If the coefficient 'a' in y = ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.