Sketch a quadratic function with the given characteristics.
1 answer:
Answer:
See photo below
Add arrows to the two ends of the parabola.
Step-by-step explanation:
To sketch this quadratic function, we to connect three dots: the two roots and a vertex.
The given roots are -1 and 1.
Draw <u>two dots at the x-intercepts</u>, which are (-1, 0) and (1, 0).
Vertex dot: V (x, y)
The vertex x-coordinate always in the middle of the two roots. The middle of -1 and 1 is 0. That's the same as the y-axis.
V (0, y)
Since the function increases when x < 0, the parabola will <u>open up</u>.
We read from left to right. The greater numbers are towards the top of the page.
<u>You can put the vertex anywhere on the y-axis that is below the x-axis.</u>
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Answer:
Step-by-step explanation:
Let
Subbing in:
a = 9, b = -2, c = -7
The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:
Group together in groups of 2:
Now factor out what's common within each set of parenthesis:
We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:
Remember that
so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.
The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring gives us that x = 1 and -1. The other set is a bit more tricky. If
then
and
You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:
±
which will simplify down to
±
Those are the 4 solutions to the quartic equation.