The vertex of this parabola is at (3, 5). When the y-value is 6, the x-value is -1. What is the coefficient of the squared term in the parabola's equation?A.4B.2C.-2D.-4SUBMITarrow_backPREVIOUS
Question
The vertex of this parabola is at (3, 5). When the y-value is 6, the x-value is -1. What is the coefficient of the squared term in the parabola's equation?A.4B.2C.-2D.-4SUBMITarrow_backPREVIOUS
Solution
The equation of a parabola in vertex form is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Given that the vertex of the parabola is at (3, 5), we can substitute h = 3 and k = 5 into the equation to get y = a(x - 3)² + 5.
We also know that when y = 6, x = -1. Substituting these values into the equation gives us 6 = a(-1 - 3)² + 5.
Solving this equation for a will give us the coefficient of the squared term in the parabola's equation.
First, simplify the equation: 6 = a(-4)² + 5, which simplifies to 6 = 16a + 5.
Subtract 5 from both sides to isolate the term with a: 1 = 16a.
Finally, divide both sides by 16 to solve for a: a = 1/16.
Therefore, none of the options A, B, C, D are correct. The coefficient of the squared term in the parabola's equation is 1/16.
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