Solving Quadratics

Front

What is the prime factorization of 75?

Back

75 = 3 × 5², thus \sqrt{75} = 5\sqrt{3}.

Front

How do you factor the quadratic expression x² - 16x + 48?

Back

The factors are (x - 12)(x - 4).

Front

What are the x-intercepts of the quadratic equation y = 3x² - 9x + 6?

Back

The x-intercepts are (1, 0) and (2, 0).

Front

How do you solve the equation (h - 2)² = 9 using square roots?

Back

h = 5 or h = -1.

Front

What is the factored form of the quadratic expression x² + 9x + 20?

Back

The factors are (x + 5)(x + 4).

Front

What is the quadratic formula?

Back

The quadratic formula is x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}.

Front

What does it mean for a quadratic equation to have real roots?

Back

A quadratic equation has real roots if the discriminant (b² - 4ac) is greater than or equal to zero.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using h = -\frac{b}{2a} and k = f(h).

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry is the vertical line x = -\frac{b}{2a}.

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.