Question

For what values of m does the graph of y 3x2 7x m have two x intercepts

Answer 1

The graph has a minimum point and is a parabola. Therefore, change the minimal value in the formula y = 3x2 + 7x + m. The value at the minimum point must be smaller than zero because the graph has two x-intercepts. The minimum point of the graph, which is a parabola, lies at x=-b/2a = -7/6.

What is Graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

The graph has a minimum point and is a parabola.

Therefore, change the minimal value in the formula y = 3x^2 + 7x + m.

The value at the minimum point must be smaller than zero because the graph has two x-intercepts.

The graph is a parabola, with x=-b/2a = -7/6 as the minimum.

3(49/36) – 49/6 + m < 0

49/12 – 49/6 + m < 0

(49-98)/12 + m < 0

-49/12 + m < 0

m < 49/12

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