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write the equation of the parabola that has its x-intercepts at (-1.6, 0) and (-3.2, 0) and its y-intercept at (0, 25.6)

User Juls
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Final answer:

The equation of the parabola can be written in the form y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a is a constant. Since the parabola has x-intercepts at (-1.6, 0) and (-3.2, 0), we know that the vertex lies on the line of symmetry. Substituting the y-intercept (0, 25.6) into the equation, we can solve for a.

Step-by-step explanation:

The equation of the parabola can be written in the form y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a is a constant.

Since the parabola has x-intercepts at (-1.6, 0) and (-3.2, 0), we know that the vertex lies on the line of symmetry, which is the average of the x-intercepts: (h = (-1.6 + -3.2)/2, k = 0).

Substituting the y-intercept (0, 25.6) into the equation gives us 25.6 = a(0 - h)² + k = ah² + k. Solving for a, we find that a = 25.6/h².

User Akshay Kumar
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