Write y= -4x^2+8x-1 in vertex form.
y= (-4x^2+8x+2+16)-1+2+16
y= (-2x+4)^2+17 (answer)
no, the coefficient of the x term inside the bracket should be 1
so
y= -4x^2+8x-1
= -4[x^2 - 2x ] - 1
= -4[x^2 - 2x + 1 - 1] - 1
= -4[(x-1)^2 - 1] - 1
= -4(x-1)^2 + 4 - 1
= -4(x-1)^2 + 3
so the vertex is (1,3)
To convert the equation y = -4x^2 + 8x - 1 into vertex form, you can follow these steps:
Step 1: Group the first two terms together.
y = (-4x^2 + 8x) - 1
Step 2: Factor out the common coefficient of x^2 and x from the grouped terms.
y = -4(x^2 - 2x) - 1
Step 3: Complete the square inside the parentheses by adding and subtracting the square of half the coefficient of x (which is -2 in this case).
y = -4(x^2 - 2x + (-2/2)^2 - (-2/2)^2) - 1
Simplifying the square term in the parentheses gives:
y = -4(x^2 - 2x + 1 - 1) - 1
Step 4: Rearrange the equation by regrouping the terms.
y = -4((x^2 - 2x + 1) - 1) - 1
Step 5: Further simplify the expression inside the parentheses.
y = -4((x - 1)^2 - 1) - 1
Step 6: Apply the distributive property to remove the parentheses.
y = -4(x - 1)^2 + 4 - 1
Simplifying gives:
y = -4(x - 1)^2 + 3
So, the vertex form of the given equation is y = -4(x - 1)^2 + 3.