Question

Write the equation of the quadratic function in standard form given the roots are 6 and -2 and a point on the graph is (10,24)

Answer 1

EXPLANATION

Since we have that the roots are (6,0) and (-2,0) and a point on the graph, the canonical quadratic equation is as follows:

$y=a(x-6)(x-(-2))$

Subtracting:

$y=a(x-6)(x+2)$

Applying the distributive property:

$y=a(x^2+2x-6x-12)$

Adding like terms:

$y=a(x^2-4x-12)$

Now, in order to compute the value of a, we must plug the point (10,24):

$24=a(10^2-4\cdot10-12)$

Multiplying numbers:

$24=a(100-40-12)$

Adding numbers:

$24=a(48)$

Dividing both sides by 48:

$\frac{24}{48}=a$

Simplifying:

$\frac{1}{2}=a$

Switching sides:

$a=\frac{1}{2}$

Plugging in a into the equation:

$y=\frac{1}{2}(x^2-4x-12)$

Applying the distributive property:

$y=\frac{1}{2}x^2-2x-6$

In conclusion, the expression of the quadratic equation is as follows:

$y=\frac{1}{2}x^2-2x-6$