a) Draw the graph of y = 2x2 - 3x − 5 for −2 otin x otin 4. b) Use the graph to solve 2x2 - 3x − 5 = 0. c)…

Question

a) Draw the graph of y = 2x2 - 3x − 5 for −2 otin x otin 4. b) Use the graph to solve 2x2 - 3x − 5 = 0. c) Using a suitable straight line, solve 2x2 - 5x − 3 = 0.

ScanSolve AI Tutor · Accepted Answer

22. Graphing and Solving Quadratic Equations a) Draw the graph of y = 2x² − 3x − 5 taking the values of x in the interval −2 ≤ x ≤ 4. Step 1: Create a table of values for y = 2x² − 3x − 5 for the given interval. y = 2x² − 3x − 5 x — 2x² — −3x — −5 — y−2 — 8 — 6 — −5 — 9 −1 — 2 — 3 — −5 — 0 0 — 0 — 0 — −5 — −5 1 — 2 — −3 — −5 — −6 2 — 8 — −6 — −5 — −3 3 — 18 — −9 — −5 — 4 4 — 32 — −12 — −5 — 15 Step 2: Plot the points from the table on the graph paper. Step 3: Draw a smooth curve through the plotted points to represent the graph of y = 2x² − 3x − 5. b) Use the graph to solve the equation 2x² − 3x − 5 = 0. To solve 2x² − 3x − 5 = 0 using the graph, find the x-intercepts of the curve y = 2x² − 3x − 5, which are the points where y=0. From the table of values and by observing where the curve crosses the x-axis: The curve crosses the x-axis at x = −1 and x = 2.5. x = −1 or 2.5; c) Using a suitable straight line, solve the equation 2x² − 5x − 3 = 0. Step 1: Relate the given equation 2x² − 5x − 3 = 0 to the graph equation y = 2x² − 3x − 5. Subtract the target equation from the graph equation: (2x² − 3x − 5) − (2x² − 5x − 3) = y − 0; 2x² − 3x − 5 − 2x² + 5x + 3 = y; 2x − 2 = y; The suitable straight line to draw is y = 2x − 2. Step 2: Create a table of values for the straight line y = 2x − 2. x — y = 2x − 2-2 — −6 0 — −2 2 — 2 4 — 6 Step 3: Plot these points and draw the straight line y = 2x − 2 on the same graph as the curve. Step 4: Identify the x-coordinates of the intersection points between the curve y = 2x² − 3x − 5 and the straight line y = 2x − 2. These x-coordinates are the solutions to 2x² − 5x − 3 = 0. By observing the intersection points on the graph, the line y = 2x − 2 intersects the curve y = 2x² − 3x − 5 at approximately x = −0.5 and x = 3. x = −0.5 or 3

$x$	$2x^2$	$-3x$	$-5$	$y$
-2	8	6	-5	9
-1	2	3	-5	0
0	0	0	-5	-5
1	2	-3	-5	-6
2	8	-6	-5	-3
3	18	-9	-5	4
4	32	-12	-5	15

$x$	$y = 2x - 2$
-2	-6
0	-2
2	2
4	6

A) Draw the graph of y = 2x2 − 3x − 5 for -2 otin x otin 4. b) Use the graph to solve 2x2 − 3x − 5 = 0. c) Using a suitable straight line, solve 2x2 − 5x − 3 = 0.

Answers

Step-by-step solution

Part a· 3 steps

Create a table of values for $y = 2x^2 - 3x - 5$ for the given interval.

Plot the points from the table on the graph paper.

Draw a smooth curve through the plotted points to represent the graph of $y = 2x^2 - 3x - 5$ .

Part b
$-1 \text{ or } 2.5$

Part c· 4 steps
$-0.5 \text{ or } 3$

Relate the given equation $2x^2 - 5x - 3 = 0$ to the graph equation $y = 2x^2 - 3x - 5$ .

Create a table of values for the straight line $y = 2x - 2$ .

Plot these points and draw the straight line $y = 2x - 2$ on the same graph as the curve.

Identify the $x$ -coordinates of the intersection points between the curve $y = 2x^2 - 3x - 5$ and the straight line $y = 2x - 2$ .

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More Mathematics Questions

Key points of y = 2x² − 3x − 5
Point	x	y
x-intercept	−1	0
y-intercept	0	−5
Minimum	0.75	−6.12
x-intercept	2.5	0

A) Draw the graph of y = 2x2 − 3x − 5 for -2 otin x otin 4. b) Use the graph to solve 2x2 − 3x − 5 = 0. c) Using a suitable straight line, solve 2x2 − 5x − 3 = 0.

Answers

Step-by-step solution

Part a· 3 steps

Create a table of values for y=2x2−3x−5y = 2x^2 - 3x - 5y=2x2−3x−5 for the given interval.

Plot the points from the table on the graph paper.

Draw a smooth curve through the plotted points to represent the graph of y=2x2−3x−5y = 2x^2 - 3x - 5y=2x2−3x−5.

Part b−1 or 2.5-1 \text{ or } 2.5−1 or 2.5

Part c· 4 steps−0.5 or 3-0.5 \text{ or } 3−0.5 or 3

Relate the given equation 2x2−5x−3=02x^2 - 5x - 3 = 02x2−5x−3=0 to the graph equation y=2x2−3x−5y = 2x^2 - 3x - 5y=2x2−3x−5.

Create a table of values for the straight line y=2x−2y = 2x - 2y=2x−2.

Plot these points and draw the straight line y=2x−2y = 2x - 2y=2x−2 on the same graph as the curve.

Identify the xxx-coordinates of the intersection points between the curve y=2x2−3x−5y = 2x^2 - 3x - 5y=2x2−3x−5 and the straight line y=2x−2y = 2x - 2y=2x−2.