Question

The minimum of a parabola is located at (-1, -3). The point (0.1) is also on the graph. Which equation can be

solved to determine the a value in the function representing the parabola?

Answer 1

Equation of a parabola in vertex form: y = a(x - h)² + k

Equation of the parabola: y = 4(x + 1)² - 3

Explanation:

• Equation of a parabola in vertex form: y = a(x - h)² + k
  where (h, k) is the vertex

Substituting the given vertex (-1, -3) into the equation:

y = a(x + 1)² - 3

As the curve passes through point (0, 1), substitute x=0 and y=1 into the equation and solve for a:

1 = a(0 + 1)² - 3

⇒ 1 = a - 3

⇒ a = 4

Therefore, y = 4(x + 1)² - 3