y=(x+4)2−7 a) Determine the x-intercepts of the quadratic equation in both approximate and exact form...

Sapewa

Sapewa

Answered

2021-12-27

y=(x+4)27
a) Determine the x-intercepts of the quadratic equation in both approximate and exact form
b) Determine the vertex point.
c) Determine the y-intercept.
d) Graph the parabola.

Answer & Explanation

Fasaniu

Fasaniu

Expert

2021-12-28Added 46 answers

Step 1 
Solution: y=(x+4)27 
(x+4)2=y+7 
1) By substituting y=0, the x intercept can be achieved.
(x+4)2=0+7 
(x+4)2=7 
x+4=±7 
x=±74 
Because of this, x intercepts are  74 and 74 
2) contrasting it with the fundamental parabola equation
(xh)2=4a(yk) 
(x+4)2=(y+7) 
h=4, k=7 
Therefore vertex is (h, k)=(4, 7) 
Step 2 
3) You can get the y intercept by changing x=0 
y=(x+4)27 
y=(0+4)27 
y=167=9 
4) (xh)2=4a(yk) 
(x+4)2=(y+7) 
4a=1 
a=14 
Therefore four of the parabola is of (0, y4) 
Also y=(x+4)27 
y=x2+16+8x7 
y=x2+8x+9 
Coefficient of x2=1Parabola opens up wards. 

temzej9

temzej9

Expert

2021-12-29Added 30 answers

Step 1
Use binomial theorem (a+b)2=a2+2ab+b2 to expand (x+4)2
y=x2+8x+167
Subtract 7 from 16 to get 9.
y=x2+8x+9
Swap sides so that all variable terms are on the left hand side.
x2+8x+9=y
Subtract y from both sides.
x2+8x+9y=0
This equation is in standard form: ax2+bx+c=0
Substitute 1 for a, 8 for b, and 9y for c in the quadratic formula, b±b24ac2a
x=8±824(9y)2
Square 8.
x=8±644(9y)2
Multiply -4 times 9y.
x=8±64+4y362
Add 64 to 36+4y.
x=8±4y+282
Take the square root of 28+4y.
1) x=8±2y+72
Now solve the equation (1) when ± is plus. Add -8 to 27+y
x=2y+782
Divide 8+27+y by 2
x=y+74
When ± is minus. Subtract 27+y by
x=y+74
The equation is now solved
x=y+74
x=y+74
karton

karton

Expert

2022-01-09Added 439 answers

Step 1
a) Write the equation in standard form
x28x+y9=0
Step 2
Substitute the values of a, b, and c into the quadratic formula
x=(8)(8)24(1)(y9)2(1) or x=(8)+(8)24(1)(y9)2(1)
Step 3
Simplify the discriminant
x=(8)4(y+7)2(1) or x=(8)+4(y+7)2(1)
Step 4
Simplify
x=y+74 or x=y+74
Step 5
b) Let's focus on:
(x+4)27
Expand the expression
x2+8x+167
Step 6
Group like terms together
x2+8x+(167)
Step 7
Add or subtract the numbers
x2+8x+9
c) Parabola equation in polynomial form
The vertex ofan up-down facing parabola of the form y=ax2+bx+c is xv=b2a
Rewrite y=(x+4)27 in the form y=ax2+bx+c
y=x2+8x+9
The parabola params are:
a=1,b=8,x=9
xv=b2a
xv=82×1
Simplify
xv=4
Plug in xv=4 to find the yv value
yv=7
Therefore the parabola vertex is
(-4, -7)
If a<0, then the vertex is a maximum value
If Pa>0, then the vertex is a minimum value
Minimum (-4, -7)
Step 8
 

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