The vertex of this parabola is at (3, -2). When the x-value is 4, they-value is 3. What is the coefficient of the squared expression in the parabola's equation?A.5B.-1C.1D.7SUBMITarrow_backPREVIOUS
Question
The vertex of this parabola is at (3, -2). When the x-value is 4, they-value is 3. What is the coefficient of the squared expression in the parabola's equation?A.5B.-1C.1D.7SUBMITarrow_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, -2), we can substitute h = 3 and k = -2 into the equation to get y = a(x - 3)² - 2.
We also know that when x = 4, y = 3. Substituting these values into the equation gives us 3 = a(4 - 3)² - 2.
Solving this equation for a will give us the coefficient of the squared expression in the parabola's equation.
3 = a(1)² - 2 3 = a - 2 a = 3 + 2 a = 5
So, the coefficient of the squared expression in the parabola's equation is 5. Therefore, the answer is A.5.
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