Rewrite each equation in vertex form by completing the square. then identify the vertex.
[tex]Rewrite each equation in vertex form by completing the square. then identify the vertex.[/tex]
Rewrite each equation in vertex form by completing the square. then identify the vertex.
[tex]Rewrite each equation in vertex form by completing the square. then identify the vertex.[/tex]
ANSWER
Vertex form:
[tex]y = 2( {x - 4)}^{2} - 27[/tex]
Vertex:
V(4,-27)
EXPLANATION
The given function is
[tex]y = 2 {x}^{2} - 16x + 5[/tex]
Complete the square as follows:
[tex]y = 2( {x}^{2} - 8x) + 5[/tex]
[tex]y = 2( {x}^{2} - 8x + 16) + 5 - 2 \times 16[/tex]
[tex]y = 2( {x - 4)}^{2} + 5 - 32[/tex]
The vertex form is:
[tex]y = 2( {x - 4)}^{2} - 27[/tex]
The vertex is:
V(4,-27)
The vertex form of the given equation is f(x) = (x+7/2)²+(-61/4) where vertex is (-7/2,-61/4).
Step-by-step explanation:
We have given a quadratic equation in standard form.
f (x)= x²+7x-3
We have to rewrite given equation in vertex form.
y = a(x-h)²+k is vertex form of equation where (h,k) is vertex of equation.
We will use method of completing square to solve this.
Adding and subtracting (7/2)² to above equation, we have
f(x) = x²+7x-3+(7/2)²-(7/2)²
f(x) = x²+7x+(7/2)²-3-(7/2)²
f(x) = (x+7/2)²-3-49/4
f(x) = (x+7/2)²+(-12-49)/4
f(x) = (x+7/2)²+(-61/4)
Hence, The vertex form of the given equation is f(x) = (x+7/2)²+(-61/4) where vertex is (-7/2,-61/4).
ANSWER
Vertex form;
[tex]y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}[/tex]
Vertex
[tex]V( - \frac{3}{2} , - \frac{35}{4} )[/tex]
EXPLANATION
Given:
[tex]f(x) = 3 {x}^{2} + 9x - 2[/tex]
We complete the square as follows:
[tex]y = 3( {x}^{2} + 3x) - 2[/tex]
[tex]y = 3( {x}^{2} + 3x + \frac{9}{4} ) - 2 - 3 \times \frac{9}{4}[/tex]
The vertex form is:
[tex]y = 3( {x + \frac{3}{2} })^{2} - \frac{35}{4}[/tex]
The vertex is
[tex]V( - \frac{3}{2} , - \frac{35}{4} )[/tex]
The vertex form of the given equation is f(x) = 3(x+3/2)²+(19/4) where vertex is (-3/2,19/4).
Step-by-step explanation:
We have given a quadratic equation in standard form.
f(x)= 3x²+9x-2
We have to rewrite given equation in vertex form.
f (x) = a(x-h)²+k is vertex form of equation where (h,k) is vertex of equation.
We will use method of completing square to solve this.
Adding and subtracting (9/2)² to above equation, we have
f(x) = 3(x²+3x)-2
f(x) = 3(x²+3x+(3/2)² ) -2+3(3/2)²
f(x) = 3(x²+3x+(3/2)² ) -2+3(9/4)
f(x) = 3(x+3/2)²-2+27/4
f(x) = 3(x+3/2)²+(-8+27)/4
f(x) = 3(x+3/2)²+(19/4)
Hence, The vertex form of the given equation is f(x) = 3(x+3/2)²+(19/4) where vertex is (-3/2,19/4).
The vertex form of the given equation is y = (x+4)²-11 where vertex is (-4,-11).
Step-by-step explanation:
We have given a quadratic equation in standard form.
y = x²+8x+5
We have to rewrite given equation in vertex form.
y = (x-h)²+k is vertex form of equation where (h,k) is vertex of equation.
We will use method of completing square to solve this.
Adding and subtracting (4)² to above equation, we have
y = x²+8x+5 +(4)²-(4)²
y = x²+8x+(4)²+5-(4)²
y = (x)²+2(x)(4)+(4)²+5-16
y = (x+4)²-11
Hence, the vertex form of the given equation is y = (x+4)²-11 where vertex is (-4,-11).
ANSWER
Vertex form:
[tex]y = ( {x + 4)}^{2} - 11[/tex]
Vertex
V(-4,-11)
EXPLANATION
The given expression is
[tex]y = {x}^{2} + 8x + 5[/tex]
We complete the square to get the vertex form.
Add and subtract half the square of the coefficient of x.
[tex]y = {x}^{2} + 8x + 16 + 5 - 16[/tex]
[tex]y = ( {x + 4)}^{2} - 11[/tex]
The vertex is
V(-4,-11)
The vertex form of the given equation is f(x) = 2(x-4)²+(-27) where vertex is (4,-27).
Step-by-step explanation:
We have given a quadratic equation in standard form.
y= 2x²-16x+5
We have to rewrite given equation in vertex form.
y = (x-h)²+k is vertex form of equation where (h,k) is vertex of equation.
We will use method of completing square to solve this.
y = 2(x²-8x)+5
Adding and subtracting (-4)² to above equation, we have
y = 2(x²-8x+(-4)²)+5-2(-4)²
y = 2(x-4)²+5-2(16)
y = 2(x-4)²+ 5 -32
y = 2(x-4)²-27
Hence, The vertex form of the given equation is f(x) = 2(x-4)²+(-27) where vertex is (4,-27).
ANSWER
Vertex form
[tex]f(x) = {( x + \frac{7}{2}) }^{2} - \frac{61}{4}[/tex]
Vertex:
[tex]V( - \frac{7}{2} , - \frac{6 1}{4} )[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} + 7x - 3[/tex]
Add and subtract the square of half the coefficient of x.
[tex]f(x) = {x}^{2} + 7x + ( { \frac{7}{2} })^{2} - 3 + ( { \frac{7}{2} })^{2}[/tex]
The vertex form is
[tex]f(x) = {( x + \frac{7}{2}) }^{2} - \frac{61}{4}[/tex]
The vertex is
[tex]V( - \frac{7}{2} , - \frac{6 1}{4} )[/tex]