Consider the parabola given by the equation: f(x) = -4x^2 +...

Consider the parabola given by the equation: $f(x) = -4x^2 + 6x + 13$ Find the following for this parabola: A) The vertex: B) The vertical intercept is the point (0, 13) C) Find the coordinates of the two $x$ intercepts of the parabola and write them as a list, separated by commas: It is OK to round your value(s) to two decimal places.

Transcript

00:01 Okay, so we're given a quadratic equation here, negative 2x squared minus 12x minus 9.

00:06 We need to find the following, starting with the vertex.

00:09 So noticing this is in standard form, we can find the x value of the vertex by using x is equal to negative b over 2a, with the understanding that when it's in standard form, highest to lowest exponents, this is our a value, this is our b value, and this is our c value.

00:28 Okay, so we would have negative negative 12 over 2 times negative 2, negative times the negative positive 12, 2 times negative 2, negative 4, 12 divided by negative 4 gives us negative 3.

00:41 So that's the x value.

00:42 To find any y value, you just plug that back in for the x's.

00:46 So negative 2 times negative 3 squared minus 12 times negative 3 minus 9.

00:54 Okay, so negative 3 squared, we get positive 9, and then negative times negative positive 12 times 3, 36 minus 9, and then negative 2 times 9, negative 18 plus 36 minus 9, so 18 minus 9 gives us 9.

01:10 So the vertex therefore would be order paired negative 3 comma positive 9.

01:19 All right, so that's our vertex.

01:24 Our axis of symmetry runs through the vertex, and it's a vertical line, so x equals negative 3.

01:31 Then it wants to know the y -intercept.

01:34 So a y -intercept is where the graph crosses the y -axis, right? so if i'm a point on the y -axis, my x value is zero.

01:41 So if i look back up here, if i plug in zeros for the x, for these x's, they would completely go away, leaving me with negative 9.

01:48 So that's the axis of symmetry...

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