Identify the family of curves represented by the equation y = a(x - h)^2 + k.
Practice Questions
Q1
Identify the family of curves represented by the equation y = a(x - h)^2 + k.
Parabolas
Circles
Ellipses
Hyperbolas
Questions & Step-by-Step Solutions
Identify the family of curves represented by the equation y = a(x - h)^2 + k.
Correct Answer: Parabolas
Step 1: Look at the equation y = a(x - h)^2 + k.
Step 2: Identify the parts of the equation: 'a' affects the direction and width of the parabola, 'h' is the horizontal shift, and 'k' is the vertical shift.
Step 3: If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.
Step 4: The vertex of the parabola is at the point (h, k).
Step 5: Since 'a', 'h', and 'k' can change, this equation represents a family of parabolas with different shapes and positions.
Quadratic Functions – The equation represents a quadratic function in vertex form, where (h, k) is the vertex of the parabola.
Parabola Orientation – The parameter 'a' determines the direction of the opening of the parabola (upwards if a > 0, downwards if a < 0).
