# Math Help - Parabola

1. ## Parabola

find the value of the discriminant: Use that number to describe the nature of the roots:

a. 12x^2+2x+5=0

b. x^2+6x=0

2: suppose f(x)=3x^2+2x1
a. find x if f(x)=7
b. find the x-intercepts
c. find f(-4)
d.find (2)

2. for $ax^2+bx+c=0$ the discriminant is $\Delta = b^2-4ac$

When

$\Delta >0$ your quadratic has two distinct real roots

$\Delta =0$ your quadratic has one repeated real root

$\Delta <0$ your quadratic has no real roots

for $12x^2+2x+5=0$ then $a = 12, b=2$ and $c = 5$

so $\Delta = 2^2-4\times 12 \times 5 = \dots$

finish this and make your conclusion.

3. Originally Posted by Kayla
find the value of the discriminant: Use that number to describe the nature of the roots:

a. 12x^2+2x+5=0

b. x^2+6x=0
Do you know that the discriminant of $ax^2+ bx+ c= 0$ is $b^2- 4ac$.

2: suppose f(x)=3x^2+2x1
was this supposed to be "+ 1"? I will assume f(x)= 3x^2+ 2x+ 1.

a. find x if f(x)=7
Solve 3x^2+ 2x+ 1= 7

b. find the x-intercepts
Those are where f(x)= 0. Solve 3x^2+ 2x+ 1= 0.

c. find f(-4)
That is just 3(-4)^2+ 2(-4)+ 1.

d.find (2)
Assuming you mean f(2), it is just 3(2)^2+ 2(2)+ 1.