Mathematics

Mathematics

Problem

State the coordinate of the y-intercept of g(x)=32x4−75x2+1110g(x)=\dfrac{3}{2}x^4-\dfrac{7}{5}x^2+\dfrac{11}{10}.
Intuitive explanation

The y-intercept is where a graph crosses the y-axis, which always happens when x=0x=0. Rather than memorizing a rule, just substitute x=0x=0 into the function—all the terms with xx vanish, leaving only the constant term. That constant is your y-intercept's y-coordinate, and the point itself always has the form (0,c)(0, c).

Intuitive explanation

The y-intercept is where a graph crosses the y-axis, which always happens when x=0x=0. Rather than memorizing a rule, just substitute x=0x=0 into the function—all the terms with xx vanish, leaving only the constant term. That constant is your y-intercept's y-coordinate, and the point itself always has the form (0,c)(0, c).

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