Part A: x = -5/4, 3 || (-5/4, 0) (3, 0)
To find the x-intercepts, we need to know where y is equal to 0. So, we will set the function equal to 0 and solve for x.
4x^2 - 7x - 15 = 0
4 x 15 = 60 || -12 x 5 = 60 || -12 + 5 = -7
4x^2 - 12x + 5x - 15 = 0
4x(x - 3) + 5(x - 3) = 0
(4x + 5)(x - 3) = 0
4x + 5 = 0
x = -5/4
x - 3 = 0
x = 3
Part B: minimum, (7/8, -289/16)
The vertex of the graph will be a minimum. This is because the parabola is positive, meaning that it opens to the top.
To find the coordinates of the parabola, we start with the x-coordinate. The x-coordinate can be found using the equation -b/2a.
b = -7
a = 4
x = -(-7) / 2(4) = 7/8
Now that we know the x-value, we can plug it into the function and solve for the y-value.
y = 4(7/8)^2 - 7(7/8) - 15
y = 4(49/64) - 49/8 - 15
y = 196/64 - 392/64 - 960/64
y = -1156/64 = -289/16 = -18 1/16
Part C:
First, start by graphing the vertex. Then, use the x-intercepts and graph those. At this point we should have three points in a sort of triangle shape. If we did it right, each of the x-values will be an equal distance from the vertex. After we have those points graphed, it is time to draw in the parabola. Knowing that the parabola is positive, we draw in a U shape that passes through each of the three points and opens toward the top of the coordinate grid.
Hope this helps!
Answer:a=2.1 :)
Step-by-step explanation:a+(-1.6)=-3.7
+1.6 +1.6
a=-2.1
Answer:
s = - 1 ± 
Step-by-step explanation:
Given
s² + 2s - 6 = 0 ( add 6 to both sides )
s² + 2s = 6
To complete the square
add ( half the coefficient of the s- term )² to both sides
s² + 2(1)s + 1 = 6 + 1
(s + 1)² = 7 ( take the square root of both sides )
s + 1 = ± ( subtract 1 from both sides )
s = - 1 ±
Thus
s = - 1 - , s = - 1 +
Answer: x=75
Explanation:
x+10+x+20=180
combine like terms
2x+30=180
subtract 30 from each side
2x=150
divide each side by 2
x=75
Answer= 36.75
3.75x 8 = 30
2.25x3= 6.75
6.75+30=36.75
