If a parabola has its vertex at (3, -2) and opens downwards, what is the general
Practice Questions
Q1
If a parabola has its vertex at (3, -2) and opens downwards, what is the general form of its equation?
y + 2 = a(x - 3)^2
y + 2 = -a(x - 3)^2
y - 2 = a(x + 3)^2
y - 2 = -a(x + 3)^2
Questions & Step-by-Step Solutions
If a parabola has its vertex at (3, -2) and opens downwards, what is the general form of its equation?
Step 1: Identify the vertex of the parabola. The vertex is given as (3, -2). Here, h = 3 and k = -2.
Step 2: Write the general form of the equation for a downward-opening parabola. The equation is y - k = -a(x - h)^2.
Step 3: Substitute the values of h and k into the equation. Replace h with 3 and k with -2.
Step 4: The equation now looks like: y - (-2) = -a(x - 3)^2.
Step 5: Simplify the equation. This gives us y + 2 = -a(x - 3)^2.
Step 6: The general form of the equation is y = -a(x - 3)^2 - 2, where 'a' is a positive number that determines how 'wide' or 'narrow' the parabola is.
Vertex Form of a Parabola – Understanding the vertex form of a parabola and how to apply it to find the equation based on the vertex coordinates.
Direction of Opening – Recognizing how the direction in which a parabola opens (upward or downward) affects the sign in the equation.
