How do you find the vertex and the intercepts for y=−2x2+13x−6?

1 Answer
Nghi N.
Apr 7, 2016

Vertex(134,1218)

Explanation:

x-coordinate of vertex:
x=−b2a=−13−4=134
y-coordinate of vertex:
y(134)=−2(16916)+13(134)−6=1698−6=1218
Vertex (134,1218)
To find y-intercept, make x = 0 --> y = -6.
To find x-intercepts, make y = 0 and solve the quadratic equation
−2x2+13x−6=0
D=d2=b2−4ac=169−48=121 --> d=±11
There are 2 real roots (x-intercepts):
x=−b2a±d2a=134±114
graph{-2x^2 + 13x - 6 [-40, 40, -20, 20]}

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