How do you find the vertex and intercepts for #f(x) = -5x^2 + 7x + 4#?

1 Answer
Nghi N.
Dec 2, 2015

Find vertex and intercepts of f(x) = - 5x^2 + 7x + 4

Explanation:

x-coordinate of vertex:
#x = (-b)/(2a) = 7/10#
y-coordinate of vertex:
#y = f(7/10) = - 49/100 + 49/10 + 4 = 645/100#
To find y-intercept, make x = 0 --> f(x) = 4
To find x-intercepts, make y = 0 and solve the quadratic equation:
#-5x^2 + 7x + 4 = 0#.
#D = d^2 = b^2 - 4ac = 49 + 80 = 129# --> #d = +- sqrt29 = +- 5.39#
#x = -7/10 +- 5.39/10 = - 0.7 - 5.39 = -6.09# and
#x = -7/10 + 5.39 = 5.39 - 0.7 = 4.69#

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