Question

Suppose you are given the function t(x) = x^2 + 8x - 20 Explain how you would graph this function, making sure to include the following information: Coordinate(s) of the solutions/rootscoordinate of the y-intercept location of the line of symmetrycoordinate of the vertex whether the graph opens up or down and how you know

Answer 1

t(x) = x² + 8x - 20

Coordinate(s) of the solutions/roots

x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0

roots: x= 2 and x = -10

coordinate of the y-intercept

y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20

y-intercept: y = -20

location of the line of symmetry

x = -4

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4

coordinate of the vertex

(-4, -36)

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)

whether the graph opens up or down and how you know

Opens up

Because the coefficient of x² is positive