If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value o

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Question: If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?

Options:

Correct Answer: 2

Solution:

Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.

If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?

If the parabola y = ax^2 + bx + c has its vertex at (1, -2), what is the value of a if it passes through the point (0, 0)?

Step 1: Understand that the vertex of the parabola is given as (1, -2). This means the parabola can be written in vertex form: y = a(x - 1)^2 - 2.
Step 2: We know the parabola passes through the point (0, 0). This means when x = 0, y should equal 0.
Step 3: Substitute x = 0 and y = 0 into the vertex form equation: 0 = a(0 - 1)^2 - 2.
Step 4: Simplify the equation: 0 = a(1) - 2, which simplifies to 0 = a - 2.
Step 5: Solve for a by adding 2 to both sides: a = 2.

Vertex Form of a Parabola – Understanding how to convert the standard form of a quadratic equation to vertex form and how to use the vertex to find the equation.
Substituting Points into Equations – The ability to substitute given points into the equation to solve for unknown coefficients.