Quadratics Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the vertex's x-coordinate.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts (or zeros) are the points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

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 equation x = -b/(2a).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as f(x) = ax^2 + bx + c.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is written as f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is written as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

How do you find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: r = (-b ± √(b² - 4ac)) / (2a).