Quadratic Equations + Features

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is called a parabola.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = (x - p)(x - q), where p and q are the roots of the equation.

Front

What is vertex form of a quadratic equation?

Back

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

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

What does the coefficient 'a' in a quadratic equation determine?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width 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 the equation x = -b/(2a) for the quadratic equation y = ax² + bx + c.

Front

How can you find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

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.