Hello, im doing this quadratics math assingment, i have not been able to resolve the next three questions. Could someone please help me out? i would be extremely grateful

1. Consider the function, f(x)= -4x^2 -16x -7
a)Determine the y-intercept
b)Determine the vertex
c) Determine the x-intercepts

(When i tried this one i converted the stantard form to vertex form, but im not sure if i did it right, and then to get the x intercepts i tried the Australian method to convert it to factored form but i failed, so im all confused now)

2. Simplify the following expression:

√18 + √20 + √12 + √32
----- ---- ---- -----
√50 √45 √75 √18

(the thing infront of the numbers is the square root sign)

3. Determine the value(s) of K, such that the quadratic equation
0= x^2 + kx + k + 15

pleasee, help i need to understand how to resolve this

2. Originally Posted by MonaMath
...

2. Simplify the following expression:

√18 + √20 + √12 + √32
----- ---- ---- -----
√50 √45 √75 √18

(the thing infront of the numbers is the square root sign)

...
You can calculate the square root partially(?):

$\dfrac{\sqrt{18}}{\sqrt{50}}+\dfrac{\sqrt{20}}{\sq rt{45}}+\dfrac{\sqrt{12}}{\sqrt{75}}+\dfrac{\sqrt{ 32}}{\sqrt{18}} =
\dfrac{\sqrt{9\cdot 2}}{\sqrt{25\cdot 2}}+\dfrac{\sqrt{4\cdot 5}}{\sqrt{9\cdot 5}}+\dfrac{\sqrt{4\cdot 3}}{\sqrt{25\cdot 3}}+\dfrac{\sqrt{16\cdot 2}}{\sqrt{9\cdot 2}}$

Now calculate the square root of the squares and cancel the common factors.

3. Originally Posted by MonaMath
Hello, im doing this quadratics math assingment, i have not been able to resolve the next three questions. Could someone please help me out? i would be extremely grateful

1. Consider the function, f(x)= -4x^2 -16x -7
a)Determine the y-intercept
b)Determine the vertex
c) Determine the x-intercepts

(When i tried this one i converted the stantard form to vertex form, but im not sure if i did it right, and then to get the x intercepts i tried the Australian method to convert it to factored form but i failed, so im all confused now)

2
Hello Mona,

(1) $f(x)=-4x^2-16x-7$

$f(x)=-4(x^2+4x+4)-7+16$

$f(x)=(x+2)^2+9$

$V(-2, 9)$

To find the y-intercept, find f(0).

$f(0)=-4(0)^2-16(0)-7=-7$

To find the zeros, set f(x)=0 and solve for x.

$-4x^2-16x-7=0$

$4x^2+16x+7=0$

$(2x+7)(2x+1)=0$

$x=-\frac{7}{2} \ \ or \ \ x=-\frac{1}{2}$