Thread: quadratics

if someone could please show me the steps to finding this, i would really appreciate it. thanx

1) A quadratic relation is given by y=ax^2+b
if the two points P(1,5) and Q(2,11) are on the graph of the relation, then find a and b.

2) A parabola is defined by the equation y=a(x-2)^2+k. the points (0,17) and (2,5) are on the curve. find the equation of the parabola.

Originally Posted by imthatgirl

if someone could please show me the steps to finding this, i would really appreciate it. thanx

1) A quadratic relation is given by y=ax^2+b
if the two points P(1,5) and Q(2,11) are on the graph of the relation, then find a and b.

You know that: y=ax^2+b

Subtract ax^2 from both sides to get: y-ax^2=b

Now substitute to get the two equations below:

b=5-a1^2=5-1a=5-a

and

b=11-a2^2=11-4a

Obviously b=b

So substitute to get: 5-a=11-4a

subtract 5 from both sides: -a=6-4a

add 4a to both sides: 3a=6

divide by 3: a=2

Now go back to equation: y=ax^2+b

Substitute: 5=(2)(1)^2+b

thus: 5=2+b

then: 3=b

Now check:

y=ax^2+b

y=2x^2+3

y=2(2)^2+3

y=2(4)+3

y=8+3

y=11

So you can see it works. Can you do the other one?

ok i get it now, thank you so much

Originally Posted by imthatgirl

if someone could please show me the steps to finding this, i would really appreciate it. thanx

1) A quadratic relation is given by y=ax^2+b
if the two points P(1,5) and Q(2,11) are on the graph of the relation, then find a and b.

2) A parabola is defined by the equation y=a(x-2)^2+k. the points (0,17) and (2,5) are on the curve. find the equation of the parabola.

Hi,

Quick has already shown to you how you get the solution you are looking for.
Here is another attempt:

1) You know values of x and y. If you plug in these values into the given general equation you'll get a linear equation for each point:

P: 5 = a*(1)² + b
Q: 11 = a*(2)² + b

P: a + b = 5
Q: 4a + b = 11

Chose the method to solve this system of linear equation you know best to get the results for a and b.

2) Only for confirmation: y = 3(x-2)²+5 = 3x²-12x+17

EB