How to solve these questions ?
A quadratic function #f(x)=ax^2 +bx +c# , where #a,b and c# are constants, has a minimum point #(2,-13)# and intersects the y-axis at #(0,-5)#
(a) Sketch the graph of the function #f(x)#
(b) Find the function #f(x)# in terms of #x#
A quadratic function
(a) Sketch the graph of the function
(b) Find the function
1 Answer
Explanation:
#(a)#
#"we can express f(x) in "color(blue)"vertex form"#
#•color(white)(x)f(x)=a(x-h)^2+k#
#"where "(h,k)" are the coordinates of the vertex and a"#
#"is a constant"#
#"here "(h,k)=(2,-13)#
#rArrf(x)=a(x-2)^2-13#
#"to find a substitute "(0,-5)" into the equation"#
#-5=4a-13rArra=2#
#rArrf(x)=2(x-2)^2-13#
#"since "a>0" then graph is "uuu#
#"plot "(0,-5),(2,-13)#
#"and draw a smooth curve through them"#
graph{2(x-2)^2-13 [-40, 40, -20, 20]}
#(b)#
#f(x)=2(x-2)^2-13#
#color(white)(f(x))=2(x^2-4x+4)-13#
#color(white)(f(x))=2x^2-8x+8-13#
#color(white)(f(x))=2x^2-8x-5larrcolor(red)" in terms of x"#