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

If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?

If the vertex of the parabola y = ax^2 + bx + c is at (1, -2), what is the value of a if b = 4 and c = -6?

Step 1: Identify the formula for the x-coordinate of the vertex of a parabola, which is x = -b/(2a).
Step 2: Substitute the given value of b (which is 4) into the formula: x = -4/(2a).
Step 3: Set the x-coordinate of the vertex (which is 1) equal to the expression from Step 2: 1 = -4/(2a).
Step 4: To eliminate the fraction, multiply both sides of the equation by 2a: 2a * 1 = -4.
Step 5: This simplifies to 2a = -4.
Step 6: Now, solve for a by dividing both sides by 2: a = -4 / 2.
Step 7: Calculate the value: a = -2.

Vertex of a Parabola – Understanding how to find the vertex of a parabola using the formula x = -b/(2a) and its relation to the coefficients a, b, and c.
Quadratic Functions – Knowledge of the standard form of a quadratic function and how to manipulate it to find specific values.