Answer:
Please check the explanation.
Step-by-step explanation:
4)
If an equation representing a parabola is in vertex form such as
[tex]y\:=a\left(x-k\right)^2+h[/tex]
then its vertex will be at (k, h).
Therefore the equation for a parabola with a vertex at (-1, 3), will have the general form
[tex]y\:=a\left(x+1\right)^2+3[/tex]
If this parabola also passes through the point (1, -5) then we can determine the 'a
' parameter.
[tex]-5\:=a\left(1+1\right)^2+3[/tex]
simplifying the equation
[tex]2^2a+3=-5[/tex]
[tex]4a+3=-5[/tex]
subtract 3 from both sides
[tex]4a+3-3=-5-3[/tex]
[tex]4a=-8[/tex]
Divide both sides by 4
[tex]\frac{4a}{4}=\frac{-8}{4}[/tex]
[tex]a=-2[/tex]
So our equation in vertex form is:
[tex]y\:=-2\left(x+1\right)^2+3[/tex]
5)
Given the expression
[tex]15n^2-6n[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c[/tex]
[tex]=15nn-6n[/tex]
[tex]\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2[/tex]
[tex]\mathrm{Rewrite\:}15\mathrm{\:as\:}3\cdot \:5[/tex]
[tex]=3\cdot \:5nn-3\cdot \:2n[/tex]
Factor out the common term 3n
[tex]=3n\left(5n-2\right)[/tex]
6)
Given the expression
[tex]2x^2+5x-10x-25[/tex]
Factor 2x²+5x: x(2x+5)
Factor -10x-25: -5(2x+5)
so the expression becomes
[tex]=x\left(2x+5\right)-5\left(2x+5\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}\left(5+2x\right)[/tex]
