How do you find the vertex and intercepts for #y=5x^2-30x+49#?

1 Answer
Nghi N.
Apr 13, 2016

Vertex (3, 4)

Explanation:

x-coordinate of vertex:
#x = -b/(2a) = 30/10 = 3#
y-coordinate of vertex:
y(3) = 5(9) - 3(30) + 49 = 45 - 90 + 49 = 4
Vertex (3, 4).
Make x = 0, y-intercept = 49.
To find x-intercepts, make y = 0 and solve the quadratic equation:
#y = 5x^2 - 30x + 49 = 0.#
#D = b^2 - 4ac = 900 - 980 = -80.#
Since D < 0, there are no real roots (no x-intercepts). Since a > 0, the parabola opens upward and is completely above the x-axis.

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