The vertex of this parabola is at (4, -3). When the x-value is 5, they-value is -6. What is the coefficient of the squared expression in the parabola's equation?A.3B.-2C.2D.-3SUBMITarrow_backPREVIOUS
Question
The vertex of this parabola is at (4, -3). When the x-value is 5, they-value is -6. What is the coefficient of the squared expression in the parabola's equation?A.3B.-2C.2D.-3SUBMITarrow_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 (4, -3), we can substitute h = 4 and k = -3 into the equation to get y = a(x - 4)² - 3.
We are also given that when x = 5, y = -6. Substituting these values into the equation gives -6 = a(5 - 4)² - 3.
Solving this equation for a will give us the coefficient of the squared expression in the parabola's equation.
-6 = a(1)² - 3 -6 = a - 3 -6 + 3 = a -3 = a
So, the coefficient of the squared expression in the parabola's equation is -3. Therefore, the answer is D. -3.
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