Final answer:
The quadratic equation h = -16t^2 + 35t + 4 graphs to a parabola opening downwards, as the negative coefficient of the t^2 term indicates this directionality. Therefore, the correct answer is Parabola opening downwards.
Step-by-step explanation:
The graph of the quadratic equation h = -16t^2 + 35t + 4 follows the shape of a parabola opening downwards. This is evident because the coefficient of the t2 term is negative (-16), which indicates the parabola opens downwards. In general, a quadratic equation of the form at2 + bt + c, where 'a', 'b', and 'c' are constants, represents a parabola.
If 'a' is positive, the parabola opens upwards, and if 'a' is negative, as in this case, the parabola opens downwards.
A parabola is a type of curve formed by the graph of a quadratic function. It's a symmetrical curve that can open upwards or downwards. The equation of a parabola in standard form is
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=
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2
+
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+
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y=ax
2
+bx+c, where
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a,
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b, and
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c are constants. If
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a>0, the parabola opens upward, and if
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<
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a<0, it opens downward. It's a fundamental shape in mathematics and physics, showing up in various applications from projectile motion to the design of satellite dishes.