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Yuki888 [10]
3 years ago
11

Write the equation in standard form of the quadratic that has a root of (3,0) and a vertex at (1,-4), then list out the values o

f a,b and c.
Mathematics
1 answer:
atroni [7]3 years ago
8 0

Answer:

a = 1, b = -2, c = -3

Step-by-step explanation:

The equation in <u>factored form</u> shows the roots with the "r" and "s" variables. Note that they are written <u>negative "r"</u> and <u>negative "s"</u> in the formula.

y = a(x - r)(x - s)

The <u>vertex is always halfway between the two roots</u>.

<------[root]--------[vertex]--------[root]---->

The vertex is at x = 1, and one root is at x = 3. The other root is at x = -1.

Write the equation in factored form to show the two roots.

y = a(x - 3)(x + 1)

<u>Substitute the vertex (1, -4)</u> into the equation. The point is written (x, y).

-4 = a(1 - 3)(1 + 1)

Solve for "a".

-4 = a(-2)(2)      Simplify within the brackets

-4 = -4a          Multiply -2 and 2. Divide both sides by -4

a = 1             Solved for "a" (and kept the variable on the left side).

<u>Substitute a = 1</u> back into the formula.

y = a(x - 3)(x + 1)

y = 1(x - 3)(x + 1)

We don't have to write multiplied by 1 though, because anything multiplied by 1 is itself.

y = (x - 3)(x + 1)

Since we are looking for "a", "b", and "c", find the equation in <u>standard form</u>.

y = ax² + bx + c

To change factored form into standard form, <u>expand</u> the brackets.

y = (x - 3)(x + 1)

y = x² + x - 3x - 3

y = x² - 2x - 3

Compare the expanded equation to y = ax² + bx + c

∴ a = 1, b = -2, c = -3

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