Find the f-coordinate of the vertex by substituting a=1 and b=−1 into f = −2ab
f=−2×1−1
Solve the equation for f
f=21
Find the y-coordinate of the vertex by evaluating the function for f=21
r=(21)2−21
Calculate
More Steps
Evaluate
(21)2−21
Rewrite the expression
221−21
Evaluate the power
41−21
Reduce fractions to a common denominator
41−2×22
Multiply the numbers
41−42
Write all numerators above the common denominator
41−2
Subtract the numbers
4−1
Use b−a=−ba=−ba to rewrite the fraction
−41
r=−41
Solution
(21,−41)
Show Solution
Solve the equation
Solve for f
Solve for r
f=21+1+4rf=21−1+4r
Evaluate
r=f2−f×1
Any expression multiplied by 1 remains the same
r=f2−f
Swap the sides of the equation
f2−f=r
Move the expression to the left side
f2−f−r=0
Substitute a=1,b=−1 and c=−r into the quadratic formula f=2a−b±b2−4ac
f=21±(−1)2−4(−r)
Simplify the expression
More Steps
Evaluate
(−1)2−4(−r)
Evaluate the power
1−4(−r)
Use the commutative property to reorder the terms
1−(−4r)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses