Graphing Quadratic Equations

Front

What is the vertex of a quadratic equation?

Back

The vertex is the highest or lowest point on the graph of a quadratic equation, represented as (h, k) in the vertex form y = a(x - h)² + k.

Front

What does the standard form of a quadratic equation look like?

Back

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

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 formula x = -b/(2a) for the equation y = ax² + bx + c.

Front

How do you find the vertex from the standard form of a quadratic equation?

Back

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

Front

What transformation occurs when you change y = x² to y = (x - 4)²?

Back

The graph is shifted right 4 units.

Front

What transformation occurs when you change y = x² to y = x² + 8?

Back

The graph is shifted up 8 units.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

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

Front

What is the formula for finding the y-intercept of a quadratic equation?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives y = c in the standard form y = ax² + bx + c.

Front

What is the difference between the vertex form and standard form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, which easily shows the vertex (h, k), while the standard form is y = ax² + bx + c, which shows the coefficients.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the coefficient 'a': if a > 0, it opens upward; if a < 0, it opens downward.