The point serves as the vertex of a quadratic function (1,6). The point is traversed by the function (-2, -3). Find the function's linear and quadratic coefficients as well as its constant team.-The quadratic coefficients is&nbsp;-The linear coefficients is&nbsp;-The constant term is

Question

The point serves as the vertex of a quadratic function (1,6). The point is traversed by the function (-2, -3). Find the function&#039;s linear and quadratic coefficients as well as its constant team.-The quadratic coefficients is&amp;nbsp;-The linear coefficients is&amp;nbsp;-The constant term is

Bella · Accepted Answer

Standard vertex form of quadratic function is y=a(x−h)2+k Where point (h,k) is vertex point. ∵ vertex point is (1,6) ∵ Substitute this point in standard vertex form y=a(x−1)2+6 =a(x−1)2+6(1) Also function pass through point (−2,−3). ∵−3=a(−2−1)2+6 ⇒−3=a⋅(−3)2+6 ⇒−3=a⋅9+6 ⇒9a=−3−6 ⇒9a=−9 ⇒a=−99 =-1 Substitute &#039;a&#039; value in equation (1) y=(−1)⋅(x−1)2+6 =−(x2+1−2x)+6 =−x2+2x−1+6 =x2+2x+5 Hence quadratic function is y=−x2 Where Quadratic coefficient =−1 Linear coefficient=2 Constant term=x2+2x+5

A quadratic function has its vertex at the point (1,6). The function passes through the point (-2, -3). Find the quadratic and linear coefficients and the constant team of the function. -The quadratic coefficients is -The linear coefficients is -The constant term is

Answered question

Answer & Explanation

New Questions in Algebra I