Rewrit the equation in vertex form. Name the vertex and y-intercept.
y=3/5^2+30x+382
I need some help do not understand these type of problems.
y = 3/5 x^2 + 30x + 382
= 3/5 (x^2 + 50x) + 382
Now come s the tricky bit. Take 1/2 of 50 and square it. Add it inside the parens, and subtract it outside the parens. Be sure to recall the 3/5 multiplier involved.
y = 3/5 (x^2 + 50x + 625) - 3/5(625) + 382
y = 3/5 (x+25)^2 + 7
(y-7) = 3/5 (x+25)
And behold: standard vertex form for a parabola.
vertex at (-25,7)
y-intercept at 382 (but we knew that from the original equation, when x=0)
oops. dropped an exponent:
(y-7) = 3/5 (x+25)^2
He is 100% correct.
Thank you for explaining problems so that one can understand. Very much appreciated.
Sure, let's start by rewriting the equation in vertex form.
The vertex form of a quadratic equation is given by: y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
Given equation: y = (3/5^2) + 30x + 382
First, let's simplify the equation:
y = (3/25) + 30x + 382
y = 3/25 + 30x + 382
y = (30x + 3/25) + 382
Now, we can rewrite the equation in vertex form:
y = 30(x + 1/50) + 382
Comparing this with the vertex form equation, we can identify the vertex and y-intercept:
Vertex: (-1/50, 382)
Y-intercept: 382
To rewrite the equation in vertex form, we need to complete the square. The equation should have the form:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
First, let's group the terms that involve x together:
y = (3/5)x^2 + 30x + 382
Now, let's factor out the coefficient of x^2 (3/5) from the first two terms:
y = (3/5)(x^2 + (5/3)(30/3)x) + 382
Next, we want to complete the square inside the parentheses. To do this, we take half of the coefficient of x, square it, and add it inside the parentheses. In this case, half of (5/3)(30/3)x is (5/6)(10)x = (25/3)x.
y = (3/5)[x^2 + (25/3)x + (25/6)^2 - (25/6)^2] + 382
Now, let's simplify inside the brackets:
y = (3/5)[(x + 25/6)^2 - (625/36)] + 382
Next, distribute the (3/5) to each term inside the square brackets:
y = (3/5)(x + 25/6)^2 - (3/5)(625/36) + 382
Simplify further:
y = (3/5)(x + 25/6)^2 - (625/60) + 382
Finally, let's combine the constants:
y = (3/5)(x + 25/6)^2 + 625/60 + 382
Simplifying the constants:
y = (3/5)(x + 25/6)^2 + (625/60) + (60/60)(382)
y = (3/5)(x + 25/6)^2 + (625 + 22,920) / 60
y = (3/5)(x + 25/6)^2 + 23,545 / 60
Now, we have the equation in vertex form:
y = (3/5)(x + 25/6)^2 + 392.42
The vertex is (-25/6, 392.42). To find the y-intercept, we set x to 0:
y = (3/5)(0 + 25/6)^2 + 392.42
y = 625/20 + 392.42
y = 31.25 + 392.42
y = 423.67
Therefore, the y-intercept is (0, 423.67).