Find the formula, in standard form y = ax2 + bx + c, for a quadratic that has roots at x = -2 and x = 7, and has leading coefficient of 1.

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The formula, in standard form y = ax^2 + bx + c, for a quadratic that has roots at x = -2 and x = 7 is y = x² - 5x + 14

Given the standard form of quadratic equation expressed as

If a quadratic that has roots at x = -2 and x = 7, then their factors will be x+ 2 and x - 7.

Taking the product of the factors will give:

f(x) = (x+2)(x-7)

f(x) = x² - 7x + 2x - 14

f(x) = x² - 5x + 14

Hence the formula, in standard form y = ax^2 + bx + c, for a quadratic that has roots at x = -2 and x = 7 is y = x² - 5x + 14

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Step-by-step explanation:

Given

and

Required

Determine the quadratic equation with a leading coefficient of 1

First, we equate both expression to 0

and  becomes

and

Multiply both expressions:

Open Brackets

Hence, the quadratic equation is:

or

step-by-step explanation:

the true ones are a b and d