Answer:
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Step-by-step explanation:
The discriminant of 0 = -2x^2 + 3 is 24 and it has 2 real solutions
<h3>How to interpret the discriminant?</h3>
The equation is given as:
0 = -2x^2 + 3
Rewrite as:
-2x^2 + 3 = 0
The discriminant of an equation is calculated using:
D = B^2 - 4AC
In this case, we have:
A = -2
B = 0
C = 3
So, we have:
D = (0)^2 - 4 * -2 * 3
Evaluate
D = 24
When the discriminant is 0 or more, then the equation has real roots
Hence, the discriminant of 0 = -2x^2 + 3 is 24 and it has 2 real solutions
Read more about quadratic functions at:
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Answer:
A) (-8, -16)
B) (0, 48)
C) (-4, 0), (-12, 0)
Step-by-step explanation:
A) the vertex is the minimum y value.
extremes of a function we get by using the first derivation and solving it for y' = 0.
y = x² + 16x + 48
y' = 2x + 16 = 0
2x = -16
x = -8
so, the vertex is at x=-8.
the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16
B) is totally simple. it is f(0) or x=0. so, y is 48.
C) is the solution of the equation for y = 0.
the solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case here
a=1
b=16
c=48
x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =
= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)
x1 = -8 + 4 = -4
x2 = -8 - 4 = -12
so the x- intercepts are (-4, 0), (-12, 0)
