Graphing Quadratics & Solving

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + 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

How can you determine the number of zeros (roots) of a quadratic function?

Back

The number of zeros can be determined using the discriminant (D = b² - 4ac). If D > 0, there are 2 real roots; D = 0 means 1 real root; D < 0 indicates no real roots.

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 (-b/2a, f(-b/2a)).

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 significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) where c is the constant term.

Front

What is the standard form of a quadratic equation?

Back

The standard form is written as ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

You can convert by completing the square on the quadratic expression.