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Write the following quadratic function in standard form that passes through

(-9, 0), (2, 0), and (1, 10)? (Use intercept form)

User ShintoTuna
by
7.6k points

1 Answer

4 votes

Answer:

To write the quadratic function in standard form, we first need to determine its intercept form.

If a quadratic function passes through the points (-9, 0), (2, 0), and (1, 10), then its intercept form can be written as:

f(x) = A(x + 9)(x - 2)

where A is a constant that we need to determine.

To find the value of A, we can substitute the coordinates of the third point into the equation:

10 = A(1 + 9)(1 - 2)

10 = -10A

Dividing by -10 on both sides, we get:

A = -1

Substituting this value of A back into the intercept form, we get:

f(x) = -(x + 9)(x - 2)

Expanding this equation, we get:

f(x) = -x^2 - 7x - 18

This is now in standard form, which is:

f(x) = ax^2 + bx + c

where a = -1, b = -7, and c = -18.

User BTMPL
by
8.0k points

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