How do you find the vertex and intercepts for y=5x2−30x+49?

1 Answer
Nghi N.
Apr 13, 2016

Vertex (3, 4)

Explanation:

x-coordinate of vertex:
x=−b2a=3010=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=5x2−30x+49=0.
D=b2−4ac=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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