How do you use the important points to sketch the graph of #y = x^2 + 4x − 21#?

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Answer 1 · 2017-04-30T01:43:01

#x#-intercepts: #(-7, 0), (3, 0)#
#y#-intercept: #(0, -21)#
vertex: #(-2, 25)#

Given: #y = x^2 + 4x - 21#

To find #y#-intercept: set #x = 0: " "y = -21#

To find #x#-intercepts: set #y = 0# and factor:

#x^2 + 4x - 21 = 0#

#(x +7)(x - 3) = 0#

#x + 7 = 0; x = -7 " and " x - 3 = 0; x = 3#

To find the vertex and axis of symmetry , put the equation in #Ax^2 + Bx + C = 0# form, let #x = (-B)/(2A)# and solve for #y#:

#x = -4/2 = -2 " "# This is the axis of symmetry

#y = (-2)^2 + 4(-2) -21 = 4 - 8 - 21 = -25#

vertex: #(-2, 25)#

graph{x^2+4x-21 [-64.4, 52.63, -28.33, 30.17]}